{"id":66904,"date":"2017-07-29T03:50:09","date_gmt":"2017-07-29T03:50:09","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=66904"},"modified":"2017-07-31T09:49:52","modified_gmt":"2017-07-31T09:49:52","slug":"math-review-of-simplifying-rational-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-simplifying-rational-expressions\/","title":{"rendered":"Math Review of Simplifying Rational Expressions"},"content":{"rendered":"

Overview<\/h3>\n

A rational expression has one polynomial in the numerator and one polynomial in the denominator, which means that the numerator is divided by the denominator.\u00a0 However, the denominator cannot be solved to zero, because division by zero is undefined.
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Definition<\/h3>\n

A statement such as (x2<\/sup> +3)\/(y +6) is a rational expression, because it has one polynomial in the numerator and one polynomial in the denominator.\u00a0 The value of x can be set to any rational number, because any number squared will be a positive number.\u00a0 However, the value of y has limits.\u00a0 It cannot be any number that equals -6, because 6-6 equals zero.\u00a0 Similarly, in the rational expression 5\/x, x cannot be solved by 0, as 5\/0 is undefined.\u00a0 In the rational expression a\/ (b-2), b cannot be solved by 2.
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Simplest Form<\/h3>\n

A rational expression is in the simplest form when the only common factors in the numerator and denominator are 1 and -1.\u00a0 Think of fractions in simplest form because their common factors have been eliminated.\u00a0 Expressions such as 6\/8 can be simplified to \u00be because 2\u00b73\/2\u00b74.\u00a0 The process is similar with rational expressions.\u00a0 For example, the expression (12y +24)\/48y can be simplified by first factoring the numerator 12y +24 to 12(y +2).\u00a0 Then the new expression is [12(y +2)]\/48y.\u00a0 Then, 12\/48 can be factored to \u00bc.\u00a0 The new expression is (y +2)\/4y.<\/p>\n

Factoring the Numerator and Denominator<\/h3>\n

Sometimes both the numerator and denominator of a rational expression need to be factored to simplest terms.\u00a0 Suppose the numerator is in the form 2x2<\/sup> +x.\u00a0 It can be factored to simplest form as x (2x +1).\u00a0 Suppose the denominator is in the form 3x2<\/sup> +2x.\u00a0 It can be factored to x (3x +2).\u00a0 The x factors cancel each other out as x\/x = 1, so the new expression is (2x +1)\/ \u00a0(3x +2). Similarly, if the numerator is in the form (a2<\/sup> \u2013 1), it can be factored to\u00a0(a +1) (a-1).\u00a0 Suppose the denominator of the expression is in the form\u00a0(2a2<\/sup>-a -1).\u00a0 It can be factored to (a -1) (2a +1) because a\u00b72a equals 2a2<\/sup>, a -2a equals \u2013a, and (-1) (1) equals -1.\u00a0 The new expression is [(a+1)(a-1)]\/[(a-1)( 2a+1).\u00a0 The (a-1)\/(a-1) factor cancels out to leave a new simplified expression, (a+1)\/(2a +1).
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Factoring Additive Inverses<\/h3>\n

Rational expressions such as (x -3)\/(3-x) are expressions where the numerator and denominator are additive inverses of each other.\u00a0 To simplify, multiply the numerator by -1 to change the form to -1(x-3).\u00a0 That flips the expression to -1(3-x)\/(3-x) or -1.     Interested in\u00a0math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year. SchoolTutoring Academy<\/a>\u00a0<\/span>is the premier educational services company for K-12 and college students. To learn more about how we help parents and students in Ottawa, ON, Canada: visit: Tutoring in Ottawa, ON<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview A rational expression has one polynomial in the numerator and one polynomial in the denominator, which means that the numerator is divided by the denominator.\u00a0 However, the denominator cannot be solved to zero, because division by zero is undefined.   Definition A statement such as (x2 +3)\/(y +6) is a rational expression, because it […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[4063,4062,4061],"class_list":["post-66904","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-denominator","tag-numerator","tag-rational-expression"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/66904","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=66904"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/66904\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=66904"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=66904"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=66904"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}