{"id":7224,"date":"2014-07-07T16:51:46","date_gmt":"2014-07-07T16:51:46","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=7224"},"modified":"2014-12-02T08:25:27","modified_gmt":"2014-12-02T08:25:27","slug":"math-review-of-multiplying-and-simplifying-rational-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-multiplying-and-simplifying-rational-expressions\/","title":{"rendered":"Math Review of Multiplying and Simplifying Rational Expressions"},"content":{"rendered":"

Overview<\/h3>\n

Rational expressions may include constants or variables in the numerator and denominator.\u00a0 If the variable is in the denominator, values of the variable that cause the denominator to equal 0 must be excluded, because division by 0 is undefined.<\/p>\n

Rational Expressions<\/h3>\n

Rational expressions can include variables or constants in the numerator or denominator.\u00a0 If both the numerator and denominator are constants, such as 2\/3 or 13\/15, they are familiar as fractions.\u00a0 Suppose the expression is x\/3, or (x + 2)\/(x + 13), or even (x2<\/sup> + 18x + 81)\/3(x + 9).\u00a0 Those are rational expressions.<\/p>\n

Figure 1:\u00a0 Rational expressions can include variables or constants in the numerator or denominator.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Avoiding Zero Denominators<\/h3>\n

If the variable is in the denominator, values of the variable that cause the denominator to equal zero must be excluded.\u00a0 For example, suppose the expression is 2\/x – 3.\u00a0 In this case, the value of x cannot equal 3, because 3 – 3 equals 0, and a rational expression 3\/0 is undefined.\u00a0 If the expression is (3x3<\/sup> + x2<\/sup> + 10)\/(x2<\/sup> + 10x + 25), the value of x cannot equal -5.<\/p>\n

Multiplying Rational Expressions<\/h3>\n

Multiplying rational expressions is similar to multiplying fractions.\u00a0 The difference is that either the numerator or the denominator or both may contain variables.\u00a0 Suppose the expression is (x – 2)\/3 \u2219 (x + 2)\/(x + 7).\u00a0 The result will be [(x + 2)(x – 2)]\/[3(x + 7)].\u00a0 In this case, x cannot equal -7.\u00a0 It doesn\u2019t really matter if x equals either 2 or -2, because the numerator can equal 0, just not the denominator.<\/p>\n

Figure 2:\u00a0 Multiplying or dividing rational expressions in symbol form.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Simplifying Rational Expressions<\/h3>\n

In order to simply rational expressions, eliminate common factors that are both in the numerator and denominator.\u00a0 Suppose that the rational expression is 10(x2<\/sup> – 144)\/5(x2<\/sup> + 24x + 144).\u00a0 It is often necessary to factor the expressions to see if anything can be eliminated.\u00a0 The numerator is 10(x + 12) (x – 12) and the denominator is 5(x + 12) (x + 12).\u00a0 The expression can be divided by [5(x +12)]\/ [5(x +12)] to result in [2(x – 12)]\/(x + 12).\u00a0 Similarly, suppose the multiplication is (x2<\/sup>-25)\/6 \u2219 3\/ (x + 5).\u00a0 The result will be [(x + 5) (x – 5)3]\/ [6(x + 5)].\u00a0 The expression can be divided by [3(x + 5]\/[3(x + 5)] to result in a simplified (x – 5)\/2.<\/p>\n

Figure 3:\u00a0 Simplifying a rational expression by factoring.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Hope, AR: visit Tutoring in Hope, AR<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Rational expressions may include constants or variables in the numerator and denominator.\u00a0 If the variable is in the denominator, values of the variable that cause the denominator to equal 0 must be excluded, because division by 0 is undefined. Rational Expressions Rational expressions can include variables or constants in the numerator or denominator.\u00a0 If […]<\/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":[2754,2755,2734,2756],"class_list":["post-7224","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-avoiding-zero-denominators","tag-multiplying-rational-expressions","tag-rational-expressions","tag-simplifying-rational-expressions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7224","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=7224"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7224\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}