{"id":60,"date":"2023-09-17T07:22:32","date_gmt":"2023-09-17T07:22:32","guid":{"rendered":"https:\/\/mathority.org\/id\/pecahan-aljabar-operasi-yang-disederhanakan-penjumlahan-pengurangan-perkalian-pembagian-latihan-yang-diselesaikan\/"},"modified":"2023-09-17T07:22:32","modified_gmt":"2023-09-17T07:22:32","slug":"pecahan-aljabar-operasi-yang-disederhanakan-penjumlahan-pengurangan-perkalian-pembagian-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/pecahan-aljabar-operasi-yang-disederhanakan-penjumlahan-pengurangan-perkalian-pembagian-latihan-yang-diselesaikan\/","title":{"rendered":"Pecahan aljabar: penyederhanaan, operasi, latihan penyelesaian,\u2026"},"content":{"rendered":"<p>Pada halaman ini kami menjelaskan apa itu pecahan aljabar, kapan pecahan tersebut setara, cara menyederhanakannya, dan cara melakukan operasi pecahan aljabar (penjumlahan, pengurangan, perkalian, dan pembagian). Selain itu, Anda akan dapat melihat latihan langkah demi langkah yang diselesaikan untuk pecahan aljabar. Singkatnya, di sini Anda akan menemukan segala sesuatu tentang pecahan aljabar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-son-las-fracciones-algebraicas\"><\/span> Apa itu pecahan aljabar? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Dalam matematika, <strong>pecahan aljabar<\/strong> adalah pecahan yang mempunyai polinomial pada pembilangnya dan polinomial lain pada penyebutnya. <\/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=\"pecahan aljabar diselesaikan\" class=\"wp-image-1594\" width=\"135\" height=\"135\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Misalnya, persamaan pecahan di atas terdiri dari pecahan aljabar karena pembilang dan penyebutnya terdiri dari polinomial. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Fracciones-algebraicas-equivalentes\"><\/span> Setara pecahan aljabar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui definisi pecahan aljabar, mari kita lihat apakah dua pecahan tersebut sama besarnya.<\/p>\n<p> Secara matematis, dua <strong>pecahan aljabar dikatakan ekuivalen<\/strong> jika syarat berikut terpenuhi: <\/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=\"contoh pecahan aljabar senilai\" class=\"wp-image-1599\" width=\"454\" height=\"55\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Sebagai contoh, kita akan memeriksa apakah 2 pecahan aljabar berikut ini ekuivalen:<\/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> Untuk menentukan apakah pecahan sama secara aljabar, kita mengalikan suku-sukunya secara melintang:<\/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> Sekarang mari kita hitung perkalian polinomial:<\/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> Kita mendapatkan ekspresi yang sama pada kedua sisi persamaan, jadi keduanya sebenarnya merupakan dua pecahan aljabar yang ekuivalen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Simplificar-fracciones-algebraicas\"><\/span> Sederhanakan pecahan aljabar <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Untuk menyederhanakan pecahan aljabar, pertama-tama Anda harus memfaktorkan polinomial-polinomial pada pembilang dan penyebutnya, kemudian menghilangkan faktor-faktor yang mempunyai kesamaan.<\/p>\n<p> Tentunya, untuk menyederhanakan pecahan aljabar, penting bagi Anda untuk mengetahui <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\">apa itu pemfaktoran polinomial<\/a><\/span><\/strong> dan cara melakukannya. Jika Anda masih belum mengetahui cara memfaktorkan polinomial atau tidak mengingatnya sepenuhnya, saya sarankan untuk membuka halaman tertaut sebelum melanjutkan, jika tidak, Anda hampir tidak akan memahami prosedurnya. Ini menjelaskan langkah demi langkah cara memfaktorkan polinomial dan, sebagai tambahan, Anda akan dapat melihat beberapa contoh dan berlatih dengan latihan yang diselesaikan.<\/p>\n<p> Sekarang mari kita lihat bagaimana pecahan aljabar disederhanakan dengan menerapkan metode pemfaktoran polinomial menggunakan sebuah contoh:<\/p>\n<ul>\n<li> Sederhanakan pecahan aljabar berikut:<\/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> Pertama, kita memfaktorkan polinomial pembilang dan penyebut pecahan:<\/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(Jika Anda tidak tahu cara memfaktorkan polinomial, lihat tautan di atas)\u2b06<\/p>\n<p> Dan setelah kita memfaktorkan polinomialnya, kita menghilangkan faktor persekutuan antara pembilang dan penyebutnya, yaitu, kita menghilangkan semua suku yang berulang:<\/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> Oleh karena itu, pecahan aljabar yang disederhanakan terlihat seperti ini:<\/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> Dalam soal ini, polinomial pecahan aljabar difaktorkan dengan mencari akar-akarnya; namun, terkadang polinomial dapat difaktorkan secara langsung dengan mengambil faktor persekutuannya (metode yang jauh lebih cepat). Di tautan ini Anda akan melihat apa artinya<a href=\"https:\/\/mathority.org\/id\/ekstrak-latihan-ekstrak-contoh-penyelesaian-faktor-umum\/\"><strong><span style=\"text-decoration: underline;\">mengambil faktor persekutuan<\/span><\/strong><\/a> dari polinomial dan Anda akan menemukan <span style=\"text-decoration: underline;\">cara menyederhanakan pecahan aljabar<\/span> menggunakan faktor persekutuan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Operaciones-con-fracciones-algebraicas\"><\/span> Operasi dengan pecahan aljabar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Seperti jenis pecahan lainnya, operasi juga dapat dilakukan dengan pecahan aljabar. Secara spesifik, pecahan aljabar dapat dijumlahkan, dikurangi, dikalikan, dan dibagi. Di bawah ini kami menjelaskan langkah demi langkah dengan contoh bagaimana setiap jenis operasi dihitung. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Suma-y-resta-de-fracciones-algebraicas\"><\/span> Penjumlahan dan pengurangan pecahan aljabar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Tata cara penjumlahan dan pengurangan pecahan aljabar pada dasarnya sama, jadi kita akan menganalisisnya bersama-sama. Pertama kita akan melihat contoh penjumlahan dua pecahan aljabar, dan di bawah ini kita akan mempelajari perbedaan metode pengurangan pecahan aljabar.<\/p>\n<h4 class=\"wp-block-heading\"> Menjumlahkan pecahan aljabar <\/h4>\n<p class=\"has-background\" id=\"block-1594a5f3-1254-4c9e-bbd8-f79bfe778fd8\" style=\"background-color:#ffebee\"> <strong>Penjumlahan pecahan aljabar<\/strong> dilakukan dengan cara yang sama seperti pada pecahan biasa: pertama-tama kurangi pecahan menjadi penyebut yang sama, lalu tambahkan pembilangnya.<\/p>\n<p id=\"block-1395699d-4152-4cd4-8029-52152aa81ba2\"> Mari kita lihat bagaimana pecahan aljabar dijumlahkan menggunakan contoh:<\/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\"> Pertama-tama kita memfaktorkan penyebut pecahan tersebut: <\/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\"> Sekarang kita perlu mencari <strong>lcm<\/strong> (kelipatan persekutuan terkecil) <strong>dari penyebutnya<\/strong> untuk mereduksi pecahan menjadi penyebut yang sama. <\/p>\n<p class=\"has-background\" id=\"block-42b361c5-dc91-4928-bf6a-cbd2d278158d\" style=\"background-color:#fffde7\"> <strong>Tip:<\/strong> KPK dari penyebut-penyebutnya selalu dibentuk dari hasil kali faktor- <strong>faktor<\/strong> <strong>persekutuannya, dikalikan dengan pangkat terbesarnya<\/strong> .<\/p>\n<p> Misalnya, dalam kasus kami<\/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> Pembagi persekutuan antara penyebut yang dipangkatkan ke pangkat terbesar adalah<\/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> Dan faktor bukan persekutuan antara penyebutnya adalah<\/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> Oleh karena itu, KPK dari penyebutnya dalam hal ini adalah:<\/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\"> Oleh karena itu, KPK dari penyebutnya adalah<\/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> oleh karena itu ini akan menjadi penyebut baru dari 2 pecahan.<\/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\"> Setelah kita menemukan penyebutnya, kita harus memodifikasi pembilangnya. Untuk melakukannya, kita mengikuti proses yang sama seperti pada penjumlahan pecahan normal: untuk setiap pecahan kita membagi 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> antara penyebut aslinya dan kalikan hasilnya dengan pembilangnya: <\/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\"> Sekarang kita dapat menggabungkan kedua pecahan tersebut karena penyebutnya sama:<\/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\"> Terakhir, kami mengoperasikan pembilangnya. Pertama-tama kita kerjakan hasil kali monomial dan polinomialnya:<\/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> Selanjutnya, kita tambahkan suku serupa ke pembilangnya:<\/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> Biasanya kita sudah sampai di sana, tapi jika kita melihat soal ini lebih dekat, kita bisa menyederhanakan pecahan aljabar lebih jauh lagi dengan menghilangkan faktor persekutuan dari pembilangnya. Belum: <\/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> Jadi kita telah menyelesaikan penjumlahan kedua pecahan aljabar tersebut.<\/p>\n<h4 class=\"wp-block-heading\"> Pengurangan pecahan aljabar <\/h4>\n<p class=\"has-background\" id=\"block-1594a5f3-1254-4c9e-bbd8-f79bfe778fd8\" style=\"background-color:#ffebee\"> Untuk <strong>mengurangkan pecahan aljabar,<\/strong> kita harus mengikuti prosedur yang mirip dengan menjumlahkan pecahan aljabar: pertama-tama kurangi pecahan tersebut menjadi penyebut yang sama, lalu kurangi pembilangnya.<\/p>\n<p id=\"block-1395699d-4152-4cd4-8029-52152aa81ba2\"> Mari kita lihat bagaimana pecahan aljabar dikurangkan dengan sebuah contoh: <\/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\"> Pertama, kita perlu memfaktorkan penyebut kedua pecahan tersebut:<\/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\"> Seperti halnya pengurangan pecahan biasa, sekarang kita harus menghitung <strong>lcm<\/strong> (kelipatan persekutuan terkecil) <strong>penyebutnya<\/strong> untuk mereduksi pecahan menjadi penyebut yang sama. Dalam hal ini, KPK dari penyebutnya adalah<\/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> oleh karena itu ini akan menjadi penyebut baru dari 2 pecahan.<\/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\"> Sekarang kita menerapkan proses yang sama seperti mengurangkan pecahan biasa: untuk setiap pecahan kita membagi 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> antara penyebut aslinya dan kalikan hasilnya dengan pembilangnya: <\/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\"> Sekarang kita gabungkan dua pecahan aljabar karena penyebutnya sama:<\/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\"> Dan kami beroperasi pada pembilangnya. Pertama-tama kita selesaikan perkalian polinomial:<\/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\"> Kesalahan yang sangat umum terjadi saat mengurangkan pecahan aljabar adalah lupa memberi tanda kurung setelah melakukan perkalian ini. Ini merupakan kesalahan karena tanda negatif mempengaruhi semua elemen hasil perkalian, bukan hanya suku pertama.<\/p>\n<p> Kami melakukan operasi dalam tanda kurung:<\/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> Jadi, berkat tanda negatifnya, kita mengubah tanda semua suku dalam tanda kurung:<\/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> Dan terakhir, kami mengelompokkan monomial serupa: <\/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> Perkalian pecahan aljabar <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Untuk <strong>mengalikan pecahan aljabar,<\/strong> pertama-tama kita memfaktorkan semua polinomial dari pecahan tersebut, kemudian kita mengalikan pembilangnya satu sama lain dan penyebutnya satu sama lain, dan terakhir kita sederhanakan pecahan yang diperoleh.<\/p>\n<p> Oleh karena itu, hasil kali pecahan aljabar sebenarnya dihitung dengan cara yang sama seperti hasil kali pecahan biasa.<\/p>\n<p> Selanjutnya mari kita lihat cara mengalikan dua pecahan aljabar dengan contoh:<\/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> Pertama-tama Anda harus memfaktorkan semua polinomial pecahan, baik pembilang maupun penyebutnya:<\/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> Sekarang mari kita mengalikan pecahan. Untuk melakukan ini, kita mengalikan pembilang dan penyebutnya:<\/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> Dan terakhir, kita sederhanakan faktor-faktor yang berulang pada penyebut dan pembilangnya:<\/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> Maka hasil perkaliannya adalah:<\/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> Pecahan tersebut tidak dapat disederhanakan lagi. Jadi kita sudah selesai mengalikan pecahan aljabar. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-de-fracciones-algebraicas\"><\/span> Pembagian pecahan aljabar <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Untuk menghitung <strong>pembagian pecahan aljabar<\/strong> , pertama-tama kita memfaktorkan semua polinomialnya, kemudian kita mengalikan pecahan tersebut secara melintang (pembilang pertama dengan penyebut kedua dan penyebut pertama dengan pembilang kedua) dan terakhir, kita menyederhanakan pecahan aljabar.<\/p>\n<p> Jadi mari kita lihat lebih baik bagaimana dua pecahan aljabar dibagi dengan menggunakan contoh:<\/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> Langkah pertama dalam membagi dua pecahan aljabar adalah dengan memfaktorkan semua polinomial yang terlibat dalam operasi tersebut:<\/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> Sekarang kita perlu membagi pecahannya. Caranya, kita mengalikan pecahan secara melintang, yaitu pembilang pertama dikalikan dengan penyebut kedua dan hasilnya adalah pembilang pecahan baru, dan dengan cara yang sama, penyebut pertama dikalikan dengan pembilang kedua. dan hasilnya adalah penyebut pecahan baru:<\/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> Mari kita sederhanakan faktor-faktor yang berulang pada penyebut dan pembilangnya:<\/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> Dan kita dapat menyederhanakan pecahan lebih jauh lagi<\/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> Pecahan tersebut tidak dapat disederhanakan lagi. Oleh karena itu, kita telah membagi pecahan aljabar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-fracciones-algebraicas\"><\/span> Latihan soal pecahan aljabar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Di bawah ini kami menawarkan kepada Anda beberapa latihan yang diselesaikan selangkah demi selangkah tentang pecahan aljabar, sehingga Anda dapat berlatih dan menyelesaikan pemahaman konsepnya. Jangan lupa Anda dapat mengajukan pertanyaan apa pun kepada kami di bawah di komentar! \ud83d\udcac\ud83d\udcac\ud83d\udcac<\/p>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan apakah pecahan aljabar berikut ekuivalen atau tidak: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk memeriksa apakah dua pecahan aljabar setara, Anda harus mengalikannya secara melintang dan melihat apakah Anda memperoleh persamaan. Jadi kita periksa dulu pecahan pertama dan kedua: <\/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\"> Kami memecahkan identitas penting di sebelah kiri persamaan:<\/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\"> Dalam hal ini, kita memperoleh persamaan, sehingga pecahan pertama dan kedua sama secara aljabar.<\/p>\n<p class=\"has-text-align-left\"> Kami sekarang menerapkan prosedur yang sama dengan pecahan aljabar pertama dan ketiga: <\/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\"> Namun kali ini pecahan aljabarnya tidak memenuhi persamaan, sehingga pecahan pertama dan ketiga berbeda secara matematis.<\/p>\n<p class=\"has-text-align-left\"> Kesimpulannya, pecahan ketiga berbeda dengan pecahan pertama sehingga juga tidak sama dengan pecahan kedua karena pecahan pertama dan kedua ekuivalen. <\/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\">Latihan 2<\/h3>\n<p> Sederhanakan pecahan aljabar berikut: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menyederhanakan pecahan aljabar, kita perlu memfaktorkan polinomial pada pembilang dan penyebutnya, lalu menghilangkan faktor berulangnya. Belum: <\/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\">Latihan 3<\/h3>\n<p> Hitung penjumlahan dan pengurangan pecahan aljabar berikut: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menjumlahkan (atau mengurangi) pecahan aljabar, pertama-tama kita harus mengurangkan pecahan tersebut menjadi penyebut yang sama, lalu menjumlahkan (atau mengurangi) pembilangnya. JADI: <\/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\">Latihan 4<\/h3>\n<p> Selesaikan perkalian dan pembagian pecahan aljabar berikut: <\/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>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mengalikan pecahan aljabar, pertama-tama kita harus memfaktorkan semua polinomialnya, kemudian mengalikan pembilang dan penyebutnya, dan terakhir menyederhanakan pecahan yang dihasilkan. <\/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\"> Sebaliknya, untuk membagi pecahan aljabar, pertama-tama kita memfaktorkan semua polinomialnya, kemudian kita mengalikan pecahan tersebut secara melintang (pembilang pertama dengan penyebut kedua dan penyebut pertama dengan pembilang kedua) dan terakhir, kita menyederhanakan pecahan aljabar yang ditemukan. <\/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> Bagaimana menurut Anda penjelasannya? Apakah kamu menyukainya? Atau apakah Anda punya saran? \ud83d\udcac Beri tahu kami pendapat Anda tentang halaman ini di komentar! Kami membacakan semuanya untuk Anda! \ud83d\udc40 Dan jangan lupa bahwa Anda juga dapat menanyakan semua pertanyaan Anda kepada kami! \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>Pada halaman ini kami menjelaskan apa itu pecahan aljabar, kapan pecahan tersebut setara, cara menyederhanakannya, dan cara melakukan operasi pecahan aljabar (penjumlahan, pengurangan, perkalian, dan pembagian). Selain itu, Anda akan dapat melihat latihan langkah demi langkah yang diselesaikan untuk pecahan aljabar. Singkatnya, di sini Anda akan menemukan segala sesuatu tentang pecahan aljabar. Apa itu pecahan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/pecahan-aljabar-operasi-yang-disederhanakan-penjumlahan-pengurangan-perkalian-pembagian-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Pecahan aljabar: penyederhanaan, operasi, latihan penyelesaian,\u2026<\/span> Selengkapnya &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":[49],"tags":[],"class_list":["post-60","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pecahan aljabar: penyederhanaan, operasi, latihan penyelesaian, dll. -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/pecahan-aljabar-operasi-yang-disederhanakan-penjumlahan-pengurangan-perkalian-pembagian-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pecahan aljabar: penyederhanaan, operasi, latihan penyelesaian, dll. -\" \/>\n<meta property=\"og:description\" content=\"Pada halaman ini kami menjelaskan apa itu pecahan aljabar, kapan pecahan tersebut setara, cara menyederhanakannya, dan cara melakukan operasi pecahan aljabar (penjumlahan, pengurangan, perkalian, dan pembagian). Selain itu, Anda akan dapat melihat latihan langkah demi langkah yang diselesaikan untuk pecahan aljabar. Singkatnya, di sini Anda akan menemukan segala sesuatu tentang pecahan aljabar. Apa itu pecahan &hellip; Pecahan aljabar: penyederhanaan, operasi, latihan penyelesaian,\u2026 Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/pecahan-aljabar-operasi-yang-disederhanakan-penjumlahan-pengurangan-perkalian-pembagian-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T07:22:32+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fractions-algebriques.jpg\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 menit\" \/>\n<script type=\"application\/ld+json\" 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