{"id":7162,"date":"2014-07-01T16:34:54","date_gmt":"2014-07-01T16:34:54","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=7162"},"modified":"2014-12-02T08:25:28","modified_gmt":"2014-12-02T08:25:28","slug":"math-review-of-division-and-reciprocals-of-rational-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/07\/01\/math-review-of-division-and-reciprocals-of-rational-expressions\/","title":{"rendered":"Math Review of Division and Reciprocals of Rational Expressions"},"content":{"rendered":"

Overview<\/h3>\n

Division of rational expressions is similar to division of real numbers. In order to divide by a rational expression, the rational expression is changed to its reciprocal, then multiplied.<\/p>\n

Reciprocals<\/h3>\n

The product of two reciprocals is 1, whether the expression is a number, a monomial with variables, or a polynomial. For example, the reciprocal of the rational expression 4\/5 is 5\/4, because 4\/5 \u2219 5\/4 is 1. The reciprocal of the monomial 3m2<\/sup> is 1\/(3m2<\/sup>), because 3m2<\/sup> times 1\/(3m2<\/sup>) is 1. Similarly, the reciprocal of the polynomial (2x2<\/sup> – 3)\/(x + 4) is (x + 4)\/(2x2<\/sup> \u2013 3).<\/p>\n

Figure 1: The product of reciprocals is 1.<\/p>\n

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

Division of Monomials<\/h3>\n

In order to divide a rational expression, multiply by the reciprocal, similar to dividing by fractions, and then simplify. Suppose 4\/5 is divided by 2\/3. In order to divide, 4\/5 is multiplied by the reciprocal of 2\/3 or 3\/2. 4\/5 times 3\/2 is 12\/10, which can be simplified to 6\/5. Similarly, suppose that (6x)\/5 is divided by (2x)\/10. The reciprocal of (2x)\/10 is 10\/(2x). 6x\/5 \u2219 10\/2x or (6x \u2219 10)\/(5 \u2219 2x), which can be further simplified to 60x\/10x or 6.<\/p>\n

Figure 2: To divide a rational expression, multiply by the reciprocal and simplify.<\/p>\n

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

Division of Rational Expressions<\/h3>\n

Suppose that (x + 1)\/(x + 2) is divided by (x – 1)\/(x + 3). The expression (x + 1)\/(x + 2) is multiplied by the reciprocal or (x + 3)\/(x – 1). The result, [(x + 1)(x + 3)]\/[(x + 2)(x – 1)] is already in simplest form. Suppose that x equals 2. Then \u00be would be divided by 1\/5, or multiplied by 5. The improper fraction 15\/4 is already in simplest terms.<\/p>\n

Division of Polynomials<\/h3>\n

Suppose that (x + 1)\/(x2<\/sup> – 1) is divided by (x + 1)\/(x2<\/sup> -2x + 1). The expression (x + 1)\/(x2<\/sup> -1) is multiplied by the reciprocal (x2<\/sup> \u2013 2x + 1)\/ (x + 1). The expression (x + 1)\/(x + 1) can be cancelled out, to leave (x2<\/sup> -2x + 1)\/(x2<\/sup> – 1). Neither expression is in simplest terms, because (x2<\/sup> -2x + 1) is the perfect square trinomial (x – 1)(x – 1) and (x2<\/sup> – 1) is the difference of squares, (x + 1)(x – 1). The expression (x – 1)\/(x – 1) can be cancelled out to leave (x-1)\/(x +1).<\/p>\n

Figure 3: The steps for the division of polynomials.<\/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 Abbotsford, BC, Canada: visit Tutoring in Abbotsford, BC, Canada<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Division of rational expressions is similar to division of real numbers. In order to divide by a rational expression, the rational expression is changed to its reciprocal, then multiplied. Reciprocals The product of two reciprocals is 1, whether the expression is a number, a monomial with variables, or a polynomial. For example, the reciprocal […]<\/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":[2733,2734,2732],"class_list":["post-7162","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-division-of-polynomials","tag-rational-expressions","tag-reciprocals"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=7162"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7162\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=7162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=7162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=7162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}