{"id":707,"date":"2013-05-28T14:42:05","date_gmt":"2013-05-28T14:42:05","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=707"},"modified":"2026-03-26T12:58:41","modified_gmt":"2026-03-26T17:58:41","slug":"simplifying-rational-polynomial-functions","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/simplifying-rational-polynomial-functions\/","title":{"rendered":"Simplifying Rational Polynomial Functions"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_V8YziAeGmnk\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_V8YziAeGmnk\" data-source-videoID=\"V8YziAeGmnk\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Simplifying Rational Polynomial Functions Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Simplifying Rational Polynomial Functions\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_V8YziAeGmnk:hover {cursor:pointer;} img#videoThumbnailImage_V8YziAeGmnk {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1139-simplifying-rational-polynomial-functions-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_V8YziAeGmnk\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_V8YziAeGmnk\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Simplifying Rational Polynomial Functions\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_V8YziAeGmnk\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_V8YziAeGmnk\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_V8YziAeGmnk\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction 7qH_Function() {\n  var x = document.getElementById(\"7qH\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"7qH_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"7qH\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example 1<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example 2<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Review\" class=\"smooth-scroll\">Review<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Simplifying_Rational_Polynomial_Function_Practice_Questions\" class=\"smooth-scroll\">Simplifying Rational Polynomial Function Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on simplifying rational polynomial functions!<\/p>\n<p>Remember, a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/rational-expressions\/\">rational expression<\/a> is a ratio of polynomial expressions, and dividing by zero is \u201cundefined,\u201d so it is really important to note that the denominator of the ratio of polynomials must never equal zero. The values of \\(x\\) that will result in a zero in the denominator are called \u201cexcluded values\u201d or <strong>\u201cdomain restrictions.\u201d<\/strong> These values must never be used in the expression.<\/p>\n<p>The notation used to represent a rational function, \\(f(x)\\), is: \\(f(x)=\\frac{p(x)}{g(x)}\\), where \\(p(x)\\) and \\(g(x)\\) are <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/polynomials\/\">polynomials<\/a>, and \\(g(x)\\neq 0\\).<\/p>\n<p>In order to simplify a rational expression, the polynomials of the numerator and the denominator must be factored, if possible, and the domain restrictions are then determined. The final step is to cancel out like factors from the numerator and denominator, because they divide to one.<\/p>\n<p>Let\u2019s look at a few examples to put this process into action. <\/p>\n<h2><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example 1<\/h2>\n<p>\nWe\u2019re going to look at:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{x^2-8x+15}{x^2-9}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis example shows a rational expression that has a trinomial in the numerator and a binomial in the denominator.  <\/p>\n<p>Now let\u2019s walk through simplifying this expression.<\/p>\n<p>First, let\u2019s factor the polynomials. So we get: \\(\\frac{(x-3)(x-5)}{(x-3)(x+3)}\\).<\/p>\n<p>Second, determine the domain restrictions from the factored denominator. The factor, \\((x-3)\\), would equal zero if \\(x=3\\). And the factor, \\((x+3)\\), would equal zero if \\(x=-3\\). So if either of these factors equals zero, then the denominator would equal zero. Therefore, the domain restrictions are \\(x=3\\) and \\(x= -3\\).<\/p>\n<p>And lastly, the factor, \\((x-3)\\), is in both the numerator and denominator. Dividing \\((x-3)\\) by itself results in 1, so these factors can be canceled out of the expression.<\/p>\n<p>Now we have the simplified rational expression, \\(\\frac{(x-5)}{(x+3)}\\), with domain restrictions of 3 and -3. Let\u2019s go through these same steps in another example.<\/p>\n<h2><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example 2<\/h2>\n<p>\nNow we\u2019re going to look at:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{x^2+10x+25}{x^2+2x-15}\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst we\u2019re going to factor the polynomials:  \\(\\frac{(x+5)(x+5)}{(x+5)(x-3)}\\).<\/p>\n<p>Then, we\u2019re going to determine the domain restrictions from the factored denominator. The factor, \\((x+5)\\), would equal zero if \\(x= -5\\). And the factor, \\((x-3)\\), would equal zero if \\(x=3\\). If either of these factors equal zero, then the denominator would equal zero. Therefore, the domain restrictions are \\(x= -5\\) and \\(x=3\\).<\/p>\n<p>And lastly, the factor, \\((x+5)\\), is in both the numerator and the denominator, so these factors cancel out of the rational expression.<\/p>\n<p>This leaves us with the simplified expression of, \\(\\frac{(x+5)}{(x-3)}\\), with domain restrictions of -5 and 3.<\/p>\n<p>The more you practice, the easier this process becomes. It is very important to note that identifying the domain restrictions in the denominator must be done immediately after factoring because the factors that are common cancel out in Step 3. (You won\u2019t be able to identify the restrictions if the factors have been canceled out!)<\/p>\n<hr>\n<h2><span id=\"Review\" class=\"m-toc-anchor\"><\/span>Review<\/h2>\n<p>\nNow, before we go, let\u2019s look at some true or false questions to test your knowledge. Feel free to pause the video to give yourself more time.<\/p>\n<p>1. True or False. The domain restrictions of this rational expression:  \\(\\frac{8x^4-28x^3+16x^2-56x}{x^2-2x-8}\\) are \\(x=4\\) and \\(x= -2\\).<\/p>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer1')\">Show Answer<\/button><\/div>\n<div id=\"Answer1\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\n<strong>The answer is true!<\/strong><\/p>\n<p style=\"text-align: left;\">Domain restrictions are determined by the factored denominator, so let\u2019s take a look at that real quick. We have the denominator \\( x^2-2x-8\\) if we factor this we get \\((x-4)(x+2)\\). The \\(x\\)-values that would make these factors equal zero are \\(x=4\\) and \\(x= -2\\).<\/p>\n<\/div>\n<p>\n&nbsp;<br \/>\n2. True or False. The rational expression \\(\\frac{3x^2+9x-12}{x^2-1}\\) simplifies to \\(\\frac{3(x+4)}{(x+1)}\\), with domain restrictions of \\(x= -4\\).<\/p>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer2')\">Show Answer<\/button><\/div>\n<div id=\"Answer2\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\n<strong>The correct answer is false!<\/strong><\/p>\n<p style=\"text-align: left;\">The expression is simplified correctly, but the domain restrictions are determined by the factored denominator, So once again, let\u2019s take a look at this. We have \\(x^{2}-1\\), which when you factor it, gives you \\((x+1)(x-1)\\).  The correct domain restrictions are, therefore, \\(x=1\\) and \\(x= -1\\).<\/p>\n<\/div>\n<p>\n&nbsp;<br \/>\nI hope this review was helpful! Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Simplifying_Rational_Polynomial_Function_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Simplifying Rational Polynomial Function Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the most simplified form of the following expression?<\/p>\n<div class=\"yellow-math-quote\">\\(\\dfrac{x^2+2x}{x^2+x-2}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-1-1\">\\(\\large{\\frac{x}{x-1}}\\), with domain restrictions \\(x=1\\) and \\(x=-2\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(\\large{\\frac{x}{x+2}}\\), with domain restrictions \\(x=1\\) and \\(x=2\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(\\large{\\frac{x+2}{x-1}}\\), with domain restrictions \\(x=-1\\) and \\(x=-2\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(\\large{\\frac{x-1}{x+2}}\\), with domain restrictions \\(x=-1\\) and \\(x=2\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When simplifying rational polynomial functions, start by factoring the numerator and denominator.<\/p>\n<p>Since a fraction would be undefined if there is a zero in the denominator, we must identify the domain restrictions, which is any \\(x\\)-value that would make the denominator equal to zero. Then, we cancel anything that is in both the numerator and the denominator since it equals 1.<\/p>\n<p>Factoring the numerator and denominator results in:<\/p>\n<p style=\"text-align: center;\">\\(\\dfrac{x(x+2)}{(x-1)(x+2)}\\)<\/p>\n<p>Look at the denominator to identify the domain restrictions, which are \\(x=1\\) and \\(x=-2\\). Then, the \\((x + 2)\\) from the numerator and denominator gets canceled, and we are left with \\(\\large{\\frac{x}{x-1}}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSimplify the following expression:<\/p>\n<div class=\"yellow-math-quote\">\\(\\dfrac{x^2-5x}{x^2-8x}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(\\large{\\frac{x}{x-8}}\\), with domain restrictions \\(x=0\\) and \\(x=8\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(\\large{\\frac{x}{x-5}}\\), with domain restrictions \\(x=0\\) and \\(x=5\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">\\(\\large{\\frac{x-5}{x-8}}\\), with domain restrictions \\(x=0\\) and \\(x=8\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(\\large{\\frac{x-8}{x-5}}\\), with domain restrictions \\(x=0\\) and \\(x=5\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To simplify an expression with polynomials in the numerator and denominator we will start by factoring:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{x(x-5)}{x(x-8)}\\)<\/p>\n<p>The domain restriction, based on the factored denominator, is \\(x=0\\) and \\(x=8\\). The \\(x\\) in the numerator and denominator are canceled, and we are left with \\(\\large{\\frac{x-5}{x-8}}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSimplify the following expression:<\/p>\n<div class=\"yellow-math-quote\">\\(\\dfrac{x^2-9}{x^2-2x-3}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(\\large{\\frac{x+1}{x+3}}\\), with domain restrictions \\(x=-1\\) and \\(x=-3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">\\(\\large{\\frac{x+3}{x+1}}\\), with domain restrictions \\(x=-1\\) and \\(x=3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(\\large{\\frac{x-3}{x+1}}\\), with domain restrictions \\(x=1\\) and \\(x=-3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(\\large{\\frac{x+3}{x-3}}\\), with domain restrictions \\(x=-3\\) and \\(x=3\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The expression can be simplified by first factoring the numerator and denominator:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{(x+3)(x-3)}{(x+1)(x-3)}\\)<\/p>\n<p>The domain restrictions are any values for \\(x\\) that would make the denominator of the rational polynomial a zero, which in this case are \\(x=-1\\) and \\(x=3\\). The \\((x\u20133)\\) factors can be canceled, since it is equal to 1, and we are left with \\(\\large{\\frac{x+3}{x+1}}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSimplify the following expression:<\/p>\n<div class=\"yellow-math-quote\">\\(\\frac{2x^2-3x+1}{x^2-1}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(\\large{\\frac{x-1}{x+1}}\\), with domain restrictions \\(x=1\\) and \\(x=-1\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(\\large{\\frac{x+1}{x-1}}\\), with domain restrictions \\(x=1\\) and \\(x=-1\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(\\large{\\frac{x-1}{2x-1}}\\), with domain restrictions \\(x=\\frac{1}{2}\\) and \\(x=1\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">\\(\\large{\\frac{2x-1}{x+1}}\\), with domain restrictions \\(x=1\\) and \\(x=-1\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>We will start by factoring the numerator and denominator of the rational polynomial expression:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{(2x-1)(x-1)}{(x+1)(x-1)}\\)<\/p>\n<p>The domain restrictions are \\(x=1\\) and \\(x=-1\\), because either of these two values would make the denominator have a factor of zero, which would make it undefined. The factors \\((x\u20131)\\) from both the numerator and denominator cancel out, because it is equal to 1 and anything times 1 is itself.<\/p>\n<p>The expression in its most simplified form is \\(\\large{\\frac{2x-1}{x+1}}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSimplify the following expression:<\/p>\n<div class=\"yellow-math-quote\">\\(\\dfrac{3x^2-16x-12}{x^2-4x-12}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(\\frac{x-6}{x+2}\\), with domain restrictions \\(x=2\\) and \\(x=-6\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(\\large{\\frac{x+2}{x-6}}\\), with domain restrictions \\(x=-2\\) and \\(x=6\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(\\large{\\frac{3x+2}{x+2}}\\), with domain restrictions \\(x=-2\\) and \\(x=6\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(\\large{\\frac{x+2}{3x+2}}\\), with domain restrictions \\(x=-\\frac{2}{3}\\) and \\(x=-2\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Start by factoring both the numerator and denominator:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{(3x+2)(x-6)}{(x+2)(x-6)}\\)<\/p>\n<p>The domain restrictions are any value for x that would make the denominator have a factor of zero. In this case, the values \\(x=-2\\) and \\(x=6\\) would make the denominator have a factor of zero.<\/p>\n<p>The factor \\((x\u20136)\\) in the numerator and denominator equals 1, so we can cancel those two factors, leaving \\(\\large{\\frac{3x+2}{x+2}}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n<p><script>\nfunction toggle(obj) {\n          var obj=document.getElementById(obj);\n          if (obj.style.display == \"block\") obj.style.display = \"none\";\n          else obj.style.display = \"block\";\n}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":100252,"parent":0,"menu_order":45,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-707","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-manipulating-expressions-1","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/707","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=707"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/707\/revisions"}],"predecessor-version":[{"id":287606,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/707\/revisions\/287606"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100252"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}