{"id":59,"date":"2023-09-17T07:22:32","date_gmt":"2023-09-17T07:22:32","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%bb%a3%e6%95%b0%e5%88%86%e6%95%b0-%e7%ae%80%e5%8c%96%e8%bf%90%e7%ae%97-%e5%8a%a0%e5%87%8f%e4%b9%98%e9%99%a4-%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0\/"},"modified":"2023-09-17T07:22:32","modified_gmt":"2023-09-17T07:22:32","slug":"%e4%bb%a3%e6%95%b0%e5%88%86%e6%95%b0-%e7%ae%80%e5%8c%96%e8%bf%90%e7%ae%97-%e5%8a%a0%e5%87%8f%e4%b9%98%e9%99%a4-%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%bb%a3%e6%95%b0%e5%88%86%e6%95%b0-%e7%ae%80%e5%8c%96%e8%bf%90%e7%ae%97-%e5%8a%a0%e5%87%8f%e4%b9%98%e9%99%a4-%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u4ee3\u6570\u5206\u6570\uff1a\u5316\u7b80\u3001\u8fd0\u7b97\u3001\u89e3\u51b3\u7ec3\u4e60\u2026\u2026"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u4ee3\u6570\u5206\u6570\u3001\u5b83\u4eec\u4f55\u65f6\u7b49\u4ef7\u3001\u5982\u4f55\u7b80\u5316\u5b83\u4eec\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u4ee3\u6570\u5206\u6570\u6267\u884c\u8fd0\u7b97\uff08\u52a0\u6cd5\u3001\u51cf\u6cd5\u3001\u4e58\u6cd5\u548c\u9664\u6cd5\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5df2\u89e3\u51b3\u7684\u4ee3\u6570\u5206\u6570\u7684\u5206\u6b65\u7ec3\u4e60\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u6709\u5173\u4ee3\u6570\u5206\u6570\u7684\u6240\u6709\u5185\u5bb9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-son-las-fracciones-algebraicas\"><\/span>\u4ec0\u4e48\u662f\u4ee3\u6570\u5206\u6570\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u4ee3\u6570\u5206\u6570<\/strong>\u662f\u5206\u5b50\u4e2d\u6709\u4e00\u4e2a\u591a\u9879\u5f0f\u3001\u5206\u6bcd\u4e2d\u6709\u53e6\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u5206\u6570\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fractions-algebriques.jpg\" alt=\"\u4ee3\u6570\u5206\u6570\u6c42\u89e3\" class=\"wp-image-1594\" width=\"135\" height=\"135\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u4e0a\u9762\u7684\u5206\u6570\u8868\u8fbe\u5f0f\u7531\u4ee3\u6570\u5206\u6570\u7ec4\u6210\uff0c\u56e0\u4e3a\u5b83\u7684\u5206\u5b50\u548c\u5206\u6bcd\u7531\u591a\u9879\u5f0f\u7ec4\u6210\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Fracciones-algebraicas-equivalentes\"><\/span>\u4ee3\u6570\u5206\u6570\u5f53\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u4ee3\u6570\u5206\u6570\u7684\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u4e24\u4e2a\u8fd9\u6837\u7684\u5206\u6570\u4f55\u65f6\u76f8\u7b49\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u8bb2\uff0c\u5982\u679c\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff0c\u4e24\u4e2a<strong>\u4ee3\u6570\u5206\u6570\u662f\u7b49\u4ef7\u7684<\/strong>\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemples-de-fractions-equivalentes-algebriques.jpg\" alt=\"\u7b49\u4ef7\u4ee3\u6570\u5206\u6570\u7684\u4f8b\u5b50\" class=\"wp-image-1599\" width=\"454\" height=\"55\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u4f5c\u4e3a\u793a\u4f8b\uff0c\u6211\u4eec\u5c06\u68c0\u67e5\u4ee5\u4e0b 2 \u4e2a\u4ee3\u6570\u5206\u6570\u662f\u5426\u7b49\u4ef7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ba3a266ca555e28002e4c27378731ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x+3}{x^2+5x+6} \\qquad \\cfrac{1}{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"167\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u786e\u5b9a\u5206\u6570\u5728\u4ee3\u6570\u4e0a\u662f\u5426\u76f8\u7b49\uff0c\u6211\u4eec\u5c06\u5b83\u4eec\u7684\u9879\u6a2a\u5411\u76f8\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-358c219d5ec5e8ba791c0f3f807d7f1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)\\cdot (x+2) = (x^2+5x+6)\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"268\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-106b457477b09880c099437a8aaebd46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x+3x+6 = x^2+5x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"242\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48884f070eddcdf12f0f4389e4a4b44d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+5x+6 = x^2+5x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"202\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5728\u65b9\u7a0b\u4e24\u8fb9\u5f97\u5230\u4e86\u76f8\u540c\u7684\u8868\u8fbe\u5f0f\uff0c\u56e0\u6b64\u5b83\u4eec\u5b9e\u9645\u4e0a\u662f\u4e24\u4e2a\u7b49\u4ef7\u7684\u4ee3\u6570\u5206\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Simplificar-fracciones-algebraicas\"><\/span>\u5316\u7b80\u4ee3\u6570\u5206\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u8981\u7b80\u5316\u4ee3\u6570\u5206\u6570\uff0c\u5fc5\u987b\u9996\u5148\u5c06\u591a\u9879\u5f0f\u7684\u5206\u5b50\u548c\u5206\u6bcd\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u6d88\u9664\u5b83\u4eec\u7684\u5171\u540c\u56e0\u5f0f\u3002<\/p>\n<p>\u663e\u7136\uff0c\u4e3a\u4e86\u7b80\u5316\u4ee3\u6570\u5206\u6570\uff0c\u60a8\u5fc5\u987b\u4e86\u89e3<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\">\u4ec0\u4e48\u662f\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3<\/a><\/span><\/strong>\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\u3002\u5982\u679c\u60a8\u4ecd\u7136\u4e0d\u77e5\u9053\u591a\u9879\u5f0f\u5982\u4f55\u56e0\u5f0f\u5206\u89e3\u6216\u4e0d\u5b8c\u5168\u8bb0\u4f4f\uff0c\u6211\u5efa\u8bae\u60a8\u5728\u7ee7\u7eed\u4e4b\u524d\u5148\u8bbf\u95ee\u94fe\u63a5\u9875\u9762\uff0c\u5426\u5219\u60a8\u5c06\u5f88\u96be\u7406\u89e3\u8be5\u8fc7\u7a0b\u3002\u5b83\u9010\u6b65\u89e3\u91ca\u4e86\u5982\u4f55\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u51e0\u4e2a\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002<\/p>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u901a\u8fc7\u5e94\u7528\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u7684\u65b9\u6cd5\u6765\u7b80\u5316\u4ee3\u6570\u5206\u6570\uff1a<\/p>\n<ul>\n<li>\u5316\u7b80\u4ee5\u4e0b\u4ee3\u6570\u5206\u6570\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d4a5d7aff1a98650ab53864b88f40f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^3+2x^2-x-2}{x^2-2x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"129\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u5bf9\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44fc5a57c780655bb62672a6bf0cf283_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x-1)(x+1)(x+2)}{(x-1)(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"164\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u2b06\uff08\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u591a\u9879\u5f0f\u5982\u4f55\u56e0\u5f0f\u5206\u89e3\uff0c\u8bf7\u67e5\u770b\u4e0a\u9762\u7684\u94fe\u63a5\uff09\u2b06<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6211\u4eec\u5c31\u6d88\u9664\u5206\u5b50\u548c\u5206\u6bcd\u4e4b\u95f4\u7684\u516c\u56e0\u5f0f\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5220\u9664\u6240\u6709\u91cd\u590d\u7684\u9879\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-efa638e7cb20b509ce8671d761fb8e7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\cancel{(x-1)}(x+1)(x+2)}{\\cancel{(x-1)}(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"164\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7b80\u5316\u7684\u4ee3\u6570\u5206\u6570\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae61b98cdf3f19dc83782b9bfc4a6809_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+1)(x+2)}{x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"109\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u4ee3\u6570\u5206\u6570\u7684\u591a\u9879\u5f0f\u901a\u8fc7\u6c42\u6839\u6765\u5206\u89e3\uff1b\u7136\u800c\uff0c\u6709\u65f6\u53ef\u4ee5\u901a\u8fc7\u91c7\u7528\u516c\u56e0\u5f0f\u76f4\u63a5\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff08\u66f4\u5feb\u7684\u65b9\u6cd5\uff09\u3002\u5728\u6b64\u94fe\u63a5\u4e2d\uff0c\u60a8\u5c06\u4e86\u89e3\u4ece\u591a\u9879\u5f0f\u4e2d<a href=\"https:\/\/mathority.org\/cn\/\u6458\u5f55-\u6458\u5f55-\u7ec3\u4e60-\u516c\u56e0\u6570-\u5df2\u89e3\u51b3\u7684\u4f8b\u5b50\/\"><strong><span style=\"text-decoration: underline;\">\u83b7\u53d6\u516c\u56e0\u5f0f\u7684<\/span><\/strong><\/a>\u542b\u4e49\uff0c\u5e76\u4e14\u60a8\u5c06\u4e86\u89e3<span style=\"text-decoration: underline;\">\u5982\u4f55\u4f7f\u7528\u516c\u56e0\u5f0f\u7b80\u5316\u4ee3\u6570\u5206\u6570<\/span>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Operaciones-con-fracciones-algebraicas\"><\/span>\u4ee3\u6570\u5206\u6570\u8fd0\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0e\u4efb\u4f55\u7c7b\u578b\u7684\u5206\u6570\u4e00\u6837\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u4ee3\u6570\u5206\u6570\u8fdb\u884c\u8fd0\u7b97\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4ee3\u6570\u5206\u6570\u53ef\u4ee5\u8fdb\u884c\u52a0\u6cd5\u3001\u51cf\u6cd5\u3001\u4e58\u6cd5\u548c\u9664\u6cd5\u3002\u4e0b\u9762\u6211\u4eec\u901a\u8fc7\u793a\u4f8b\u9010\u6b65\u89e3\u91ca\u6bcf\u79cd\u64cd\u4f5c\u7684\u8ba1\u7b97\u65b9\u5f0f\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Suma-y-resta-de-fracciones-algebraicas\"><\/span>\u4ee3\u6570\u5206\u6570\u7684\u52a0\u6cd5\u548c\u51cf\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4ee3\u6570\u5206\u6570\u7684\u52a0\u6cd5\u548c\u51cf\u6cd5\u7684\u8fc7\u7a0b\u5b9e\u9645\u4e0a\u662f\u76f8\u540c\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u5b83\u4eec\u653e\u5728\u4e00\u8d77\u5206\u6790\u3002\u9996\u5148\u6211\u4eec\u5c06\u770b\u5230\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\u76f8\u52a0\u7684\u4f8b\u5b50\uff0c\u4e0b\u9762\u6211\u4eec\u5c06\u7814\u7a76\u4ee3\u6570\u5206\u6570\u76f8\u51cf\u65b9\u6cd5\u7684\u533a\u522b\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u6dfb\u52a0\u4ee3\u6570\u5206\u6570<\/h4>\n<p class=\"has-background\" id=\"block-1594a5f3-1254-4c9e-bbd8-f79bfe778fd8\" style=\"background-color:#ffebee\"><strong>\u4ee3\u6570\u5206\u6570\u7684\u52a0\u6cd5<\/strong>\u4e0e\u666e\u901a\u5206\u6570\u7684\u52a0\u6cd5\u76f8\u540c\uff1a\u9996\u5148\u5c06\u5206\u6570\u5316\u7b80\u4e3a\u516c\u5206\u6bcd\uff0c\u7136\u540e\u5c06\u5206\u5b50\u76f8\u52a0\u3002<\/p>\n<p id=\"block-1395699d-4152-4cd4-8029-52152aa81ba2\">\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u4ee3\u6570\u5206\u6570\u662f\u5982\u4f55\u76f8\u52a0\u7684\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27852f0123fcecbe8be07c1cbe492d1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{x^2+2x+1} + \\cfrac{3x}{x^2+x}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"163\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p id=\"block-3672173b-c7e6-44a1-8522-63b08b168ddb\">\u6211\u4eec\u9996\u5148\u5bf9\u5206\u6570\u7684\u5206\u6bcd\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d76a27785a43860878e20f9f19f8d85f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{(x+1)(x+1)} + \\cfrac{3x}{x(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"197\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae0b117b67b96ab97cc34f0395452809_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{(x+1)^2} + \\cfrac{3x}{x(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"151\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-816f8d98-19a3-4b75-8c9f-21fc82303588\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u627e\u5230<strong>\u5206\u6bcd\u7684<\/strong><strong>lcm<\/strong> \uff08\u6700\u5c0f\u516c\u500d\u6570\uff09\uff0c\u4ee5\u5c06\u5206\u6570\u51cf\u5c11\u5230\u516c\u5206\u6bcd\u3002 <\/p>\n<p class=\"has-background\" id=\"block-42b361c5-dc91-4928-bf6a-cbd2d278158d\" style=\"background-color:#fffde7\"><strong>\u63d0\u793a\uff1a<\/strong>\u5206\u6bcd\u7684 lcm \u59cb\u7ec8\u7531<strong>\u5b83\u4eec\u7684\u5171\u540c\u56e0\u5b50\u4e58\u4ee5\u6700\u5927\u6307\u6570<\/strong>\u4e58\u4ee5<strong>\u975e\u5171\u540c\u56e0\u5b50\u7684<\/strong>\u4e58\u79ef\u5f62\u6210\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae0b117b67b96ab97cc34f0395452809_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{(x+1)^2} + \\cfrac{3x}{x(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"151\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6700\u5927\u6307\u6570\u7684\u5206\u6bcd\u4e4b\u95f4\u7684\u516c\u7ea6\u6570\u662f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-431f3a0fe905f53a3bba14fdcd2184c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+1)^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5206\u6bcd\u4e4b\u95f4\u7684\u975e\u516c\u56e0\u6570\u662f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9cc293b28f198c32e0356b52e2e23bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\u5206\u6bcd\u7684 lcm \u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d532daf990ee1d21f27629c90976a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+1)^2 \\cdot x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-436a726a-70a7-40da-a208-7769b5622363\">\u56e0\u6b64\uff0c\u5206\u6bcd\u7684 lcm \u4e3a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61abd769b2c8924619fc1de9990437b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+1)^2 \\cdot x,\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u8fd9\u5c06\u662f\u4e24\u4e2a\u5206\u6570\u7684\u65b0\u5206\u6bcd\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ac9ff4f5390125209474030fdbc2a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{(x+1)^2} + \\cfrac{3x}{x(x+1)} \\ \\longrightarrow \\ \\cfrac{}{x(x+1)^2} + \\cfrac{}{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"371\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-3640c36e-b28c-4faa-8152-67d85f2974c6\">\u4e00\u65e6\u6211\u4eec\u627e\u5230\u4e86\u5171\u540c\u70b9\uff0c\u6211\u4eec\u5c31\u5fc5\u987b\u4fee\u6539\u5206\u5b50\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9075\u5faa\u4e0e\u6b63\u6001\u5206\u6570\u76f8\u52a0\u76f8\u540c\u7684\u8fc7\u7a0b\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u5206\u6570\uff0c\u6211\u4eec\u9664\u4ee5 lcm<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-657731178831ef2525fd245d9ca550b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl( \\ x(x+1)^2 \\ \\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -7px;\"><\/p>\n<p>\u539f\u59cb\u5206\u6bcd\u4e4b\u95f4\u5e76\u5c06\u7ed3\u679c\u4e58\u4ee5\u5206\u5b50\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f7789228cada95f0a43a23b00ee3e1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x(x+1)^2}{(x+1)^2} = \\cfrac{x\\cancel{(x+1)^2}}{\\cancel{(x+1)^2}} = \\color{red}\\bm{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"230\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-85ce335cfa9eeb59efcc2ea66bb7fc0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x(x+1)^2}{x(x+1)}= \\cfrac{\\cancel{x}(x+1)^\\cancel{2}}{\\cancel{x}\\cancel{(x+1)}}=\\color{blue} \\bm{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"265\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64f36b1034879522e19c809ed07216aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{(x+1)^2} + \\cfrac{3x}{x(x+1)} \\ \\longrightarrow \\ \\cfrac{x \\cdot \\color{red}\\bm{x} \\color{black} }{x(x+1)^2} + \\cfrac{3x \\cdot \\color{blue} \\bm{(x+1)} \\color{black}}{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"483\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-eb2ac5b7-1160-4287-8f77-09fa899a0782\">\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u5c06\u4e24\u4e2a\u5206\u6570\u653e\u5728\u4e00\u8d77\uff0c\u56e0\u4e3a\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u5206\u6bcd\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2cb949a7a18557fb88da6579adfa641_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2+3x(x+1)}{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"113\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-bda62c37-98b4-4d75-94f5-69cd7d6b2a00\">\u6700\u540e\uff0c\u6211\u4eec\u5bf9\u5206\u5b50\u8fdb\u884c\u64cd\u4f5c\u3002\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u5355\u9879\u5f0f\u548c\u591a\u9879\u5f0f\u7684\u4e58\u79ef\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3572c0c661f3766c98fec0ea7bef241a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2 +3x\\cdot x+ 3x\\cdot 1 }{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da3f5de85cee840ea70185242cd4e56d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2 +3x^2 + 3x }{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"107\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u76f8\u4f3c\u7684\u9879\u6dfb\u52a0\u5230\u5206\u5b50\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0569c5469be3e30f70b75ca5cb648e19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4x^2 + 3x }{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"73\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u901a\u5e38\u60c5\u51b5\u4e0b\u6211\u4eec\u5df2\u7ecf\u5230\u4e86\u90a3\u91cc\uff0c\u4f46\u662f\u5982\u679c\u6211\u4eec\u4ed4\u7ec6\u7814\u7a76\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ece\u5206\u5b50\u4e2d\u5220\u9664\u4e00\u4e2a\u516c\u56e0\u5b50\u6765\u8fdb\u4e00\u6b65\u7b80\u5316\u4ee3\u6570\u5206\u6570\u3002\u7136\u800c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3a36483296f8ccd582c06b3d6f656df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x(4x + 3)}{x(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"74\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe08e4b3b69fc920878413f5f35724e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\cancel{x}(4x + 3)}{\\cancel{x}(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"74\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d320996e579c62a49d8a244591243d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4x + 3}{(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"63\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u5df2\u7ecf\u5b8c\u6210\u4e86\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\u7684\u548c\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4ee3\u6570\u5206\u6570\u51cf\u6cd5<\/h4>\n<p class=\"has-background\" id=\"block-1594a5f3-1254-4c9e-bbd8-f79bfe778fd8\" style=\"background-color:#ffebee\">\u8981<strong>\u51cf\u53bb\u4ee3\u6570\u5206\u6570\uff0c<\/strong>\u6211\u4eec\u5fc5\u987b\u9075\u5faa\u4e0e\u6dfb\u52a0\u4ee3\u6570\u5206\u6570\u7c7b\u4f3c\u7684\u8fc7\u7a0b\uff1a\u9996\u5148\u5c06\u5206\u6570\u51cf\u5c11\u5230\u516c\u5206\u6bcd\uff0c\u7136\u540e\u51cf\u53bb\u5206\u5b50\u3002<\/p>\n<p id=\"block-1395699d-4152-4cd4-8029-52152aa81ba2\">\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u4ee3\u6570\u5206\u6570\u662f\u5982\u4f55\u51cf\u6cd5\u7684\uff1a <\/p>\n<p class=\"has-text-align-center\" id=\"block-626dfe43-b064-405b-a4e5-64f8f9d2f3b8\">\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-230f5d12513bd0aa34943bf0bd1bc662_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x}{x^2-x-6} - \\cfrac{4x-3}{(x+2)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"167\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-3672173b-c7e6-44a1-8522-63b08b168ddb\">\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5206\u89e3\u4e24\u4e2a\u5206\u6570\u7684\u5206\u6bcd\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7203a6355aa93738a6e4da82bc98b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x}{(x+2)(x-3)} - \\cfrac{4x-3}{(x+2)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"195\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-816f8d98-19a3-4b75-8c9f-21fc82303588\">\u4e0e\u6b63\u6001\u5206\u6570\u7684\u51cf\u6cd5\u4e00\u6837\uff0c\u6211\u4eec\u73b0\u5728\u5fc5\u987b\u8ba1\u7b97<strong>\u5206\u6bcd\u7684<\/strong><strong>lcm<\/strong> \uff08\u6700\u5c0f\u516c\u500d\u6570\uff09\uff0c\u4ee5\u5c06\u5206\u6570\u51cf\u5c11\u5230\u516c\u5206\u6bcd\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5206\u6bcd\u7684 lcm \u662f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ef9edba310262ed53634436be5c90ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+2)^2(x-3) ,\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"120\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u8fd9\u5c06\u662f\u4e24\u4e2a\u5206\u6570\u7684\u65b0\u5206\u6bcd\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79f2882bb4ddf2035540641da2bd5db9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x}{(x+2)(x-3)} - \\cfrac{4x-3}{(x+2)^2} \\ \\longrightarrow \\ \\cfrac{}{(x+2)^2(x-3)} + \\cfrac{}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"504\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-3640c36e-b28c-4faa-8152-67d85f2974c6\">\u73b0\u5728\u6211\u4eec\u5e94\u7528\u4e0e\u51cf\u53bb\u6b63\u5e38\u5206\u6570\u76f8\u540c\u7684\u8fc7\u7a0b\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u5206\u6570\uff0c\u6211\u4eec\u9664\u4ee5 lcm<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-657731178831ef2525fd245d9ca550b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl( \\ x(x+1)^2 \\ \\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -7px;\"><\/p>\n<p>\u539f\u59cb\u5206\u6bcd\u4e4b\u95f4\u5e76\u5c06\u7ed3\u679c\u4e58\u4ee5\u5206\u5b50\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9d52f52e2bff5eace93764529daef0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+2)^2(x-3)}{(x+2)(x-3)} = \\cfrac{(x+2)^{\\cancel{2}}\\cancel{(x-3)}}{\\canel{(x+2)}\\cancel{(x-3)}} = \\color{red}\\bm{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"348\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2846ba14540fe74dd89606e3a527840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+2)^2(x-3)}{(x+2)^2}= \\cfrac{\\cancel{(x+2)^2}(x-3)}{\\cancel{(x+2)^2}}=\\color{blue} \\bm{x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"355\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d0cf478a0cf48972d8610efeebc10cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x}{(x+2)(x-3)} - \\cfrac{4x-3}{(x+2)^2} \\ \\longrightarrow \\ \\cfrac{2x\\cdot \\color{red}\\bm{(x+2)} \\color{black}}{(x+2)^2(x-3)} + \\cfrac{(4x-3)\\cdot \\color{blue} \\bm{(x-3)} \\color{black}}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"580\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-eb2ac5b7-1160-4287-8f77-09fa899a0782\">\u6211\u4eec\u73b0\u5728\u8fde\u63a5\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\uff0c\u56e0\u4e3a\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u5206\u6bcd\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76d9503723192264d7c0525f1dc5a762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x(x+2)-(4x-3)(x-3)}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"213\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p id=\"block-bda62c37-98b4-4d75-94f5-69cd7d6b2a00\">\u6211\u4eec\u5bf9\u5206\u5b50\u8fdb\u884c\u64cd\u4f5c\u3002\u6211\u4eec\u9996\u5148\u6c42\u89e3\u591a\u9879\u5f0f\u4e58\u6cd5\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a0a7d0ab0b62fced99150257d2646d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x^2+4x-\\bigl[4x^2-12x-3x+9\\bigr]}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"252\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\">\u4ee3\u6570\u5206\u6570\u51cf\u6cd5\u65f6\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\u9519\u8bef\u662f\u5728\u6267\u884c\u4e58\u6cd5\u540e\u5fd8\u8bb0\u52a0\u62ec\u53f7\u3002\u8fd9\u5c06\u662f\u4e00\u4e2a\u9519\u8bef\uff0c\u56e0\u4e3a\u8d1f\u53f7\u5f71\u54cd\u4e58\u79ef\u7684\u6240\u6709\u7ed3\u679c\u5143\u7d20\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u7b2c\u4e00\u9879\u3002<\/p>\n<p>\u6211\u4eec\u6267\u884c\u62ec\u53f7\u5185\u7684\u8fd0\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-afa68a0ebcbad358f5454b2d98a1b813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x^2+4x-\\bigl[4x^2-15x+9\\bigr]}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"211\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u8d1f\u53f7\uff0c\u6211\u4eec\u6539\u53d8\u4e86\u62ec\u53f7\u4e2d\u6240\u6709\u9879\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dedff86768aa41641373644dbd64e9c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x^2+4x-4x^2+15x-9}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"196\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u7c7b\u4f3c\u7684\u5355\u9879\u5f0f\u5206\u7ec4\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c622a1e2620a264cb373c3b0e37b164d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-2x^2+19x-9}{(x+2)^2(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"129\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Multiplicacion-de-fracciones-algebraicas\"><\/span>\u4ee3\u6570\u5206\u6570\u7684\u4e58\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u4e3a\u4e86<strong>\u5c06\u4ee3\u6570\u5206\u6570\u76f8\u4e58\uff0c<\/strong>\u6211\u4eec\u9996\u5148\u5c06\u6240\u8ff0\u5206\u6570\u7684\u6240\u6709\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u5c06\u5206\u5b50\u5f7c\u6b64\u76f8\u4e58\uff0c\u4ee5\u53ca\u5206\u6bcd\u5f7c\u6b64\u76f8\u4e58\uff0c\u6700\u540e\uff0c\u6211\u4eec\u7b80\u5316\u6240\u83b7\u5f97\u7684\u5206\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4ee3\u6570\u5206\u6570\u7684\u4e58\u79ef\u5b9e\u9645\u4e0a\u4e0e\u6b63\u89c4\u5206\u6570\u7684\u4e58\u79ef\u7684\u8ba1\u7b97\u65b9\u5f0f\u76f8\u540c\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u5c06\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\u76f8\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3c8c26c3bbb6d88c38bf4c8ef88da96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x}{x^2+x-2} \\cdot \\cfrac{x^2-6x+5}{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"185\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u60a8\u5fc5\u987b\u5bf9\u5206\u6570\u7684\u6240\u6709\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u5305\u62ec\u5206\u5b50\u548c\u5206\u6bcd\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05d90fbe961a4a9cb043923b03dad497_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x}{(x-1)(x+2)} \\cdot \\cfrac{(x-1)(x-5)}{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"233\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u4e58\u4ee5\u5206\u6570\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u5206\u5b50\u548c\u5206\u6bcd\u76f8\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-722813021488c38da6ce48b4a52e8d57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x \\cdot (x-1)(x-5)}{(x-1)(x+2)\\cdot (x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"177\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-184ba5c9f9ac4c307273d787e8448d83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x(x-1)(x-5)}{(x-1)(x+2)(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"164\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u7b80\u5316\u5206\u6bcd\u548c\u5206\u5b50\u4e2d\u91cd\u590d\u7684\u56e0\u5b50\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e62697ec3544aa9fd4d668c8e6e8594_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x\\cancel{(x-1)}(x-5)}{\\cancel{(x-1)}(x+2)(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"164\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u4e58\u6cd5\u7684\u7ed3\u679c\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-768cd7cd7f16a3c0481bfff2b1a56943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x(x-5)}{(x+2)(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"109\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u4e0d\u80fd\u8fdb\u4e00\u6b65\u7b80\u5316\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u5df2\u7ecf\u5b8c\u6210\u4e86\u4ee3\u6570\u5206\u6570\u7684\u4e58\u6cd5\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-de-fracciones-algebraicas\"><\/span>\u4ee3\u6570\u5206\u6570\u9664\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u4e3a\u4e86\u8ba1\u7b97<strong>\u4ee3\u6570\u5206\u6570\u7684\u9664\u6cd5<\/strong>\uff0c\u6211\u4eec\u9996\u5148\u5bf9\u6240\u6709\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u5c06\u8fd9\u4e9b\u5206\u6570\u6a2a\u5411\u76f8\u4e58\uff08\u7b2c\u4e00\u4e2a\u5206\u5b50\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u5206\u6bcd\uff0c\u7b2c\u4e00\u4e2a\u5206\u6bcd\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u5206\u5b50\uff09\uff0c\u6700\u540e\uff0c\u6211\u4eec\u7b80\u5316\u4ee3\u6570\u5206\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u793a\u4f8b\u66f4\u597d\u5730\u4e86\u89e3\u5982\u4f55\u9664\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6d69f56a5f8e07ece76cd2cc7af7758_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^3-7x-6}{2x^2-8} : \\cfrac{x^2+2x+1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"196\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u9664\u4ee5\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\u7684\u7b2c\u4e00\u6b65\u662f\u5206\u89e3\u8fd0\u7b97\u4e2d\u6d89\u53ca\u7684\u6240\u6709\u591a\u9879\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-545baef30b02392b2ff48771efc53723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+1)(x+2)(x-3)}{2(x-2)(x+2)} : \\cfrac{(x+1)^2}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"243\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u9700\u8981\u9664\u4ee5\u5206\u6570\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u5206\u6570\u6a2a\u5411\u76f8\u4e58\uff0c\u5373\u7b2c\u4e00\u4e2a\u5206\u5b50\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u5206\u6bcd\uff0c\u7ed3\u679c\u5c06\u662f\u65b0\u5206\u6570\u7684\u5206\u5b50\uff0c\u540c\u6837\uff0c\u7b2c\u4e00\u4e2a\u5206\u6bcd\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u5206\u5b50\u7ed3\u679c\u5c06\u662f\u65b0\u5206\u6570\u7684\u5206\u6bcd\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4acdd6cd4da76cb20c3cadc6a5c1d43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+1)(x+2)(x-3)\\cdot 6}{2(x-2)(x+2)\\cdot (x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"193\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b7212e50bbac42806205c19de22a0551_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6(x+1)(x+2)(x-3)}{2(x-2)(x+2)(x+1)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"180\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u7b80\u5316\u5206\u6bcd\u548c\u5206\u5b50\u4e2d\u91cd\u590d\u7684\u56e0\u5b50\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dae6e61f3285d1b55fb0aaac1b46137a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6\\cancel{(x+1)}\\cancel{(x+2)}(x-3)}{2(x-2)\\cancel{(x+2)}(x+1)^\\cancel{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"180\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-601bd6bee2dbd9229822ee5ed1200709_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6(x-3)}{2(x-2)(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"118\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u7b80\u5316\u5206\u6570\uff0c\u56e0\u4e3a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1672db950e496c9affb548df70351d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6:2 = 3.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"69\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44d5a5ff05275fd0222ff8c0569fdcba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3(x-3)}{(x-2)(x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"109\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u4e0d\u80fd\u8fdb\u4e00\u6b65\u7b80\u5316\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5df2\u7ecf\u9664\u4ee3\u6570\u5206\u6570\u4e86\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-fracciones-algebraicas\"><\/span>\u89e3\u51b3\u4e86\u4ee3\u6570\u5206\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0b\u9762\u6211\u4eec\u4e3a\u60a8\u63d0\u4f9b\u51e0\u9053\u4ee3\u6570\u5206\u6570\u7684\u9010\u6b65\u89e3\u7b54\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u60a8\u901a\u8fc7\u7ec3\u4e60\u6765\u5b8c\u6210\u5bf9\u6982\u5ff5\u7684\u7406\u89e3\u3002\u4e0d\u8981\u5fd8\u8bb0\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u7684\u8bc4\u8bba\u4e2d\u5411\u6211\u4eec\u8be2\u95ee\u60a8\u7684\u4efb\u4f55\u95ee\u9898\uff01 \ud83d\udcac\ud83d\udcac\ud83d\udcac<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u786e\u5b9a\u4e0b\u5217\u4ee3\u6570\u5206\u6570\u662f\u5426\u7b49\u4ef7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f740b5268b9119666bd42176a4f86842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x+3}{x^2-9} \\qquad \\cfrac{1}{x-3} \\qquad \\cfrac{x-3}{x^2+2x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"254\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u68c0\u67e5\u4e24\u4e2a\u4ee3\u6570\u5206\u6570\u662f\u5426\u76f8\u7b49\uff0c\u5fc5\u987b\u5c06\u5b83\u4eec\u6a2a\u5411\u76f8\u4e58\uff0c\u770b\u770b\u662f\u5426\u76f8\u7b49\u3002\u6240\u4ee5\u6211\u4eec\u9996\u5148\u68c0\u67e5\u7b2c\u4e00\u4e2a\u548c\u7b2c\u4e8c\u4e2a\u5206\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9318b0a40cd808d3abda878dc008bbd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x+3}{x^2-9}= \\cfrac{1}{x-3} \\quad ?\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"140\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c81610b6d1d22e9611f533266d69b825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)\\cdot (x-3)=(x^2-9)\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"227\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6c42\u89e3\u65b9\u7a0b\u5de6\u8fb9\u7684\u663e\u7740\u6052\u7b49\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2818cb76662004522c70eea92249fad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=x^2-9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"120\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u2705<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u7b49\u5f0f\uff0c\u56e0\u6b64\u7b2c\u4e00\u4e2a\u548c\u7b2c\u4e8c\u4e2a\u5206\u6570\u5728\u4ee3\u6570\u4e0a\u662f\u76f8\u7b49\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u5bf9\u7b2c\u4e00\u548c\u7b2c\u4e09\u4ee3\u6570\u5206\u6570\u5e94\u7528\u76f8\u540c\u7684\u8fc7\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ac874c5337fab5f612e80957bc114410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x+3}{x^2-9}= \\cfrac{x-3}{x^2+2x-3} \\quad ?\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"189\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-919a4415bd1fdb158fa2d85693fdc234_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)\\cdot (x^2+2x-3)=(x^2-9)\\cdot(x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"321\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d03f74b88827f2678256a955e86489de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+2x^2-3x+3x^2+6x-9=x^3-3x^2-9x+27\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"397\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-405dbd6c82dedfdad2ffafa7e39caff0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+5x^2+3x-9=x^3-3x^2-9x+27\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"308\" style=\"vertical-align: -2px;\"><\/p>\n<p> \u274c<\/p>\n<p class=\"has-text-align-left\">\u7136\u800c\uff0c\u8fd9\u6b21\u4ee3\u6570\u5206\u6570\u4e0d\u6ee1\u8db3\u65b9\u7a0b\uff0c\u56e0\u6b64\u7b2c\u4e00\u548c\u7b2c\u4e09\u5206\u6570\u5728\u6570\u5b66\u4e0a\u662f\u4e0d\u540c\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u603b\u4e4b\uff0c\u7b2c\u4e09\u5206\u6570\u4e0e\u7b2c\u4e00\u5206\u6570\u4e0d\u540c\uff0c\u56e0\u6b64\u5b83\u4e5f\u4e0d\u7b49\u4e8e\u7b2c\u4e8c\u5206\u6570\uff0c\u56e0\u4e3a\u7b2c\u4e00\u5206\u6570\u548c\u7b2c\u4e8c\u5206\u6570\u662f\u7b49\u4ef7\u7684\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-081129bba98116bf2c3236379c5fe973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x+3}{x^2-9} = \\cfrac{1}{x-3} \\neq \\cfrac{x-3}{x^2+2x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"230\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u5316\u7b80\u4ee5\u4e0b\u4ee3\u6570\u5206\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa89ac8c0a9e92441f00f58652927ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\cfrac{5x^2+10x}{11x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"105\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82ba94360c06faf6048680b225f02cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\cfrac{x^2-4}{x^2+2x-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"117\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb654d3fdf52ba7fce13cd0a69acc692_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\cfrac{x^3-2x^2-3x}{x^2-3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abecf1c451ad906e117a46855f5cd7cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\cfrac{x^3-3x+2}{x^3+4x^2+x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"157\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7b80\u5316\u4ee3\u6570\u5206\u6570\uff0c\u6211\u4eec\u9700\u8981\u5c06\u591a\u9879\u5f0f\u7684\u5206\u5b50\u548c\u5206\u6bcd\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u6d88\u9664\u91cd\u590d\u7684\u56e0\u5f0f\u3002\u7136\u800c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f06c8f3d861d237ca41232418bd3e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{array}{l} \\cfrac{5x^2+10x}{11x} =\\cfrac{5x(x+2)}{11x} = \\\\[4ex] =\\cfrac{5\\cancel{x}(x+2)}{11\\cancel{x}}= \\cfrac{\\bm{5(x+2)}}{\\bm{11}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"235\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f9577181669de9b9760dfe7ed8425e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{array}{l} \\cfrac{x^2-4}{x^2+2x-8} = \\cfrac{(x-2)(x+2)}{(x-2)(x+4)}= \\\\[4ex] = \\cfrac{\\cancel{(x-2)}(x+2)}{\\cancel{(x-2)}(x+4)}=\\cfrac{\\bm{x+2}}{\\bm{x+4}}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"283\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-04505e35cce382f2905db108961c6718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{array}{l} \\cfrac{x^3-2x^2-3x}{x^2-3x} =  \\cfrac{x(x+1)(x-3)}{x(x-3)}}= \\\\[4ex] = \\cfrac{\\cancel{x} (x+1) \\cancel{x-3}}{\\cancel{x}\\cancel{(x-3)}} = \\cfrac{x+1}{1} = \\\\[4ex] = \\bm{x+1}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"149\" width=\"311\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68ca63836b70d9aa6731e3271247d681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{array}{l} \\cfrac{x^3-3x+2}{x^3+4x^2+x-6}=\\cfrac{(x-1)^2(x+2)}{(x-1)(x+3)(x+2)}= \\\\[4ex] = \\cfrac{(x-1)^{\\cancel{2}}\\cancel{(x+2)}}{\\cancel{(x-1)}(x+3)\\cancel{(x+2)}}=\\cfrac{\\bm{x-1}}{\\bm{x+3}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"378\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u4ee3\u6570\u5206\u6570\u7684\u52a0\u6cd5\u548c\u51cf\u6cd5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a96e5be1d4a8e7b216abe3f5a2bc0ddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\cfrac{4}{x^2+2x} + \\cfrac{3x-2}{x^2-x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"191\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25e21ca9e99469748c58da61755e32ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\cfrac{4x}{x^3+2x^2+x} - \\cfrac{2}{x^2-3x-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"239\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-125740a48e020b23010873f17905c6ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\cfrac{7x}{x^2-4x+4} + \\cfrac{-5}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"181\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59ba454283d08de8fcc2e15d4967b00f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ x +\\cfrac{-3x}{x^2-4}  -  \\cfrac{2x^3-1}{2x^2+6x+4}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"230\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u6dfb\u52a0\uff08\u6216\u51cf\u53bb\uff09\u4ee3\u6570\u5206\u6570\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u5c06\u5206\u6570\u51cf\u5c11\u5230\u4e00\u4e2a\u516c\u5206\u6bcd\uff0c\u7136\u540e\u6dfb\u52a0\uff08\u6216\u51cf\u53bb\uff09\u5206\u5b50\u3002\u6240\u4ee5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6524d97070ae44570c7bbd75df0b6bb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{array}{l} \\cfrac{4}{x^2+2x} + \\cfrac{3x-2}{x^2-x-6} = \\cfrac{4}{x(x+2)} + \\cfrac{3x-2}{(x+2)(x-3)} = \\\\[4ex] =\\cfrac{4\\cdot(x-3)}{x(x+2)\\cdot (x-3)} + \\cfrac{(3x-2)\\cdot x}{(x+2)(x-3)\\cdot x} = \\cfrac{4\\cdot(x-3) + (3x-2)\\cdot x}{x(x+2)(x-3)} = \\\\[4ex] = \\cfrac{4x-12 + 3x^2-2x}{x(x+2)(x-3)} = \\cfrac{  \\bm{3x^2+2x-12}}{\\bm{x(x+2)(x-3)}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"175\" width=\"572\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b228a6d7ced30d4dfdca7fa7653cec0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{array}{l} \\cfrac{4x}{x^3+2x^2+x} - \\cfrac{2}{x^2-3x-4} = \\cfrac{4x}{x(x+1)^2} - \\cfrac{2}{(x+1)(x-4)}= \\\\[4ex] = \\cfrac{4x \\cdot (x-4)}{x(x+1)^2 \\cdot (x-4)} - \\cfrac{2 \\cdot (x+1) \\cdot x}{(x+1)^2(x-4)\\cdot x}= \\cfrac{4x \\cdot (x-4) - 2 \\cdot (x+1) \\cdot x }{x(x+1)^2 (x-4) }= \\\\[4ex] = \\cfrac{4x^2 -16x - 2 \\cdot (x^2+x) }{x(x+1)^2 (x-4) }= \\cfrac{4x^2 -16x - 2x^2 - 2x }{x(x+1)^2  (x-4) } =\\\\[4ex] =\\cfrac{2x^2 -18x}{x(x+1)^2 (x-4)}=\\cfrac{x(2x -18)}{x(x+1)^2 (x-4)}= \\\\[4ex] = \\cfrac{\\bm{2x -18}}{\\bm{(x+1)^2 (x-4)}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"307\" width=\"609\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-541ca3698314f502dae6b4144ff2180e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{array}{l}\\cfrac{7x}{x^2-4x+4} + \\cfrac{-5}{x-2}=\\cfrac{7x}{(x-2)^2} + \\cfrac{-5}{x-2}} = \\\\[4ex] = \\cfrac{7x}{(x-2)^2} + \\cfrac{-5\\cdot (x-2)}{(x-2)\\cdot (x-2)}=\\cfrac{7x}{(x-2)^2} + \\cfrac{-5\\cdot (x-2)}{(x-2)^2}= \\\\[4ex] = \\cfrac{7x + [-5\\cdot (x-2)] }{(x-2)^2}  =\\cfrac{7x -5\\cdot (x-2) }{(x-2)^2} = \\\\[4ex] = \\cfrac{7x -5x+10 }{(x-2)^2} = \\cfrac{ \\bm{2x+10}}{\\bm{(x-2)^2 } } \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"242\" width=\"495\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eba4fb225a87d253ea56ae18460f89a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\  \\begin{array}{l}  x +\\cfrac{-3x}{x^2-4}  -  \\cfrac{2x^3-1}{2x^2+6x+4}=\\cfrac{x}{1} +\\cfrac{-3x}{x^2-4}  -  \\cfrac{2x^3-1}{2x^2+6x+4}= \\\\[4ex] =x +\\cfrac{-3x}{(x-2)(x+2)}  -  \\cfrac{2x^3-1}{2(x+1)(x+2)}= \\\\[4ex] = \\cfrac{x\\cdot 2(x-2)(x+2)(x+1)}{1\\cdot 2(x-2)(x+2)(x+1)} \\ + \\ \\cfrac{-3x\\cdot 2(x+1)}{(x-2)(x+2)\\cdot 2(x+1)} \\ - \\  \\cfrac{(2x^3-1)\\cdot(x-2)}{2(x+1)(x+2)\\cdot (x+1)}= \\\\[4ex] = \\cfrac{ 2x(x-2)(x+2)(x+1)}{2(x-2)(x+2)(x+1)} \\ + \\ \\cfrac{-6x(x+1)}{2(x-2)(x+2)(x+1)} \\ - \\ \\cfrac{(2x^3-1)\\cdot(x-2)}{2(x-2)(x+2)(x+1)}= \\\\[4ex]= \\cfrac{ 2x^4+2x^3-8x^2-8x}{2(x-2)(x+2)(x+1)} \\ + \\ \\cfrac{-6x^2-6x}{2(x-2)(x+2)(x+1)} \\ - \\  \\cfrac{2x^4-4x^3-x+2}{2(x-2)(x+2)(x+1)} = \\\\[4ex] = \\cfrac{ 2x^4+2x^3-8x^2-8x -6x^2-6x  -  (2x^4-4x^3-x+2)}{2(x-2)(x+2)(x+1)} = \\\\[4ex] = \\cfrac{ 2x^4+2x^3-8x^2-8x -6x^2-6x  - 2x^4+4x^3+x-2}{2(x-2)(x+2)(x+1)} = \\\\[4ex] = \\cfrac{ \\bm{6x^3-14x^2-13x-2}}{\\bm{2(x-2)(x+2)(x+1)}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"508\" width=\"711\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u6c42\u89e3\u4ee5\u4e0b\u4ee3\u6570\u5206\u6570\u7684\u4e58\u6cd5\u548c\u9664\u6cd5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d07300122444585669fcc2bf1b8d1e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\cfrac{x^2+5x+4}{7}\\cdot \\cfrac{x-1}{x^2-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa1e3c21cf05605c6a408df67189bd41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\cfrac{3x^2+15x+18}{3x}\\cdot \\cfrac{x^2+x-2}{x^3+3x^2-x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"287\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e9ff7ee82098d3295e3f3911f2e1ff8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\cfrac{3x}{x^2+10x+25}:\\cfrac{2x}{x^2-25}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"209\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6534e92d7d90ee190d64290189008587_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\cfrac{x^2+8x+15}{4x}:\\cfrac{x^2+4x-5}{2x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"233\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u4e58\u4ee3\u6570\u5206\u6570\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u5bf9\u6240\u6709\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u5c06\u5206\u5b50\u548c\u5206\u6bcd\u76f8\u4e58\uff0c\u6700\u540e\u7b80\u5316\u6240\u5f97\u5206\u6570\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cc9600c8e95d957e9004296306ea25fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{array}{l} \\cfrac{x^2+5x+4}{7}\\cdot \\cfrac{x-1}{x^2-1} = \\cfrac{(x+1)(x+4)}{7}\\cdot \\cfrac{x-1}{(x-1)(x+1)}\\\\[4ex] =\\cfrac{(x+1)(x+4)\\cdot (x-1)}{7 \\cdot (x-1)(x+1)}=\\cfrac{(x+1)(x+4) (x-1)}{7(x-1)(x+1)} = \\\\[4ex] = \\cfrac{\\cancel{(x+1)}(x+4)\\cancel{ (x-1)}}{7\\cancel{(x-1)}\\cancel{(x+1)}} = \\cfrac{\\bm{x+4}}{\\bm{7}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"452\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-71554d3bb6d51cfd8c3202606ca1e6e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{array}{l}\\cfrac{3x^2+15x+18}{3x}\\cdot \\cfrac{x^2+x-2}{x^3+3x^2-x-3} = \\cfrac{3(x+2)(x+3)}{3x}\\cdot \\cfrac{(x-1)(x+2)}{(x-1)(x+1)(x+3)}= \\\\[4ex] =\\cfrac{3(x+2)(x+3)\\cdot (x-1)(x+2)}{3x\\cdot (x-1)(x+1)(x+3)}=\\cfrac{3(x+2)(x+3) (x-1)(x+2)}{3x (x-1)(x+1)(x+3)} = \\\\[4ex] = \\cfrac{\\cancel{3}(x+2)\\cancel{(x+3)} \\cancel{(x-1)}(x+2)}{\\cancel{3}x \\cancel{(x-1)}(x+1)\\cancel{(x+3)}} = \\cfrac{(x+2)(x+2)}{x (x+1)} = \\\\[4ex] = \\cfrac{\\bm{(x+2)^2}}{\\bm{x (x+1)}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"244\" width=\"636\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u4e3a\u4e86\u9664\u4ee3\u6570\u5206\u6570\uff0c\u6211\u4eec\u9996\u5148\u5bf9\u6240\u6709\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u5c06\u8fd9\u4e9b\u5206\u6570\u6a2a\u5411\u76f8\u4e58\uff08\u7b2c\u4e00\u4e2a\u5206\u5b50\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u5206\u6bcd\uff0c\u7b2c\u4e00\u4e2a\u5206\u6bcd\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u5206\u5b50\uff09\uff0c\u6700\u540e\uff0c\u6211\u4eec\u7b80\u5316\u627e\u5230\u7684\u4ee3\u6570\u5206\u6570\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8994adaa1df1f24822c8102c0d1e69c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{array}{l} \\cfrac{3x}{x^2+10x+25}:\\cfrac{2x}{x^2-25}= \\cfrac{3x}{(x+5)^2}:\\cfrac{2x}{(x-5)(x+5)}=\\\\[4ex] = \\cfrac{3x\\cdot (x-5)(x+5)}{(x+5)^2\\cdot 2x}=\\cfrac{3x(x-5)(x+5)}{2x(x+5)^2 }= \\\\[4ex] =\\cfrac{3\\cancel{x}(x-5)\\cancel{(x+5)}}{2\\cancel{x}(x+5)^\\cancel{2}} = \\cfrac{\\bm{3(x-5)}}{\\bm{2(x+5)}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"175\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-961a9787bca20a2482c010586614793d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{array}{l} \\cfrac{x^2+8x+15}{4x}:\\cfrac{x^2+4x-5}{2x^2} = \\cfrac{(x+3)(x+5)}{4x}:\\cfrac{(x-1)(x+5)}{2x^2}= \\\\[4ex] = \\cfrac{(x+3)(x+5)\\cdot 2x^2 }{4x \\cdot (x-1)(x+5)} = \\cfrac{2x^2 (x+3)(x+5)}{4x (x-1)(x+5)} = \\\\[4ex] = \\cfrac{2x^{\\cancel{2}}(x+3)\\cancel{ (x+5)}}{4\\cancel{x} (x-1)\\cancel{ (x+5)}} =\\cfrac{2x(x+3)}{4(x-1)} =  \\cfrac{\\bm{x(x+3)}}{\\bm{2(x-1)}}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"524\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p>\u4f60\u89c9\u5f97\u8fd9\u4e2a\u89e3\u91ca\u600e\u4e48\u6837\uff1f\u4f60\u559c\u6b22\u5b83\u5417\uff1f\u6216\u8005\u60a8\u6709\u4ec0\u4e48\u5efa\u8bae\u5417\uff1f \ud83d\udcac \u5728\u8bc4\u8bba\u4e2d\u544a\u8bc9\u6211\u4eec\u60a8\u5bf9\u6b64\u9875\u9762\u7684\u770b\u6cd5\uff01\u6211\u4eec\u8bfb\u4e86\u4f60\u4eec\u5168\u90e8\uff01 \ud83d\udc40 \u4e0d\u8981\u5fd8\u8bb0\uff0c\u60a8\u4e5f\u53ef\u4ee5\u5411\u6211\u4eec\u8be2\u95ee\u6240\u6709\u95ee\u9898\uff01 \u2754\ud83d\udc47\u2754\ud83d\udc47<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u4ee3\u6570\u5206\u6570\u3001\u5b83\u4eec\u4f55\u65f6\u7b49\u4ef7\u3001\u5982\u4f55\u7b80\u5316\u5b83\u4eec\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u4ee3\u6570\u5206\u6570\u6267\u884c\u8fd0\u7b97\uff08\u52a0\u6cd5\u3001\u51cf\u6cd5\u3001\u4e58\u6cd5\u548c\u9664 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%bb%a3%e6%95%b0%e5%88%86%e6%95%b0-%e7%ae%80%e5%8c%96%e8%bf%90%e7%ae%97-%e5%8a%a0%e5%87%8f%e4%b9%98%e9%99%a4-%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u4ee3\u6570\u5206\u6570\uff1a\u5316\u7b80\u3001\u8fd0\u7b97\u3001\u89e3\u51b3\u7ec3\u4e60\u2026\u2026<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-59","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized 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