{"id":66936,"date":"2017-10-16T02:18:55","date_gmt":"2017-10-16T02:18:55","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=66936"},"modified":"2017-10-16T02:20:57","modified_gmt":"2017-10-16T02:20:57","slug":"math-review-of-adding-rational-expressions-with-like-denominators","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2017\/10\/16\/math-review-of-adding-rational-expressions-with-like-denominators\/","title":{"rendered":"Math Review of Adding Rational Expressions with Like Denominators"},"content":{"rendered":"

Overview<\/strong><\/h3>\n

Adding and subtracting rational expressions with like denominators is similar to adding and subtracting fractions with like denominators.\u00a0 It is a three-step process: first add the numerators, then simplify the numerator, then simplify the result by factoring.\u00a0 Since subtraction is the inverse of addition, subtraction is a matter of adding the inverse of the numerator.<\/p>\n

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Adding with Variables in Common<\/strong><\/h3>\n

Suppose the problem is 4x\/5 + 6x\/5.\u00a0 Since the numerators have a variable in common, 4x +6x can be added as 10x.\u00a0 Then (10x)\/5 has the common factor of 5 in both the numerator and denominator.\u00a0 The simplified result is (2x)\/1, or 2x.\u00a0 Suppose there were no variable in the expression.\u00a0 It would then be a fraction, so that 4\/5 +6\/5 would equal 10\/5 or 2.<\/p>\n

<\/h3>\n

Adding with Variables in the Numerators and Denominator<\/strong><\/h3>\n

Suppose the problem is (8y2<\/sup>)\/(y +3) + (2y2<\/sup>)\/(y+3).\u00a0 The numerators have variables, and so do the denominators.\u00a0 In this case, the denominator in each expression is the same, so the numerators can be added as 8y2<\/sup> +2y2<\/sup> =10y2<\/sup>.\u00a0 The expression is then (10y2<\/sup>\/(y +3).\u00a0 There are no factors in common, so it is already in simplest terms.<\/p>\n

Adding, then Factoring<\/strong><\/h3>\n

Suppose the problem is (x2<\/sup>-4x-10)\/(x-7) +(x-18)\/(x-7).\u00a0 The denominator is the same for both rational expressions, so the numerators can be added.\u00a0 Combining like terms, (x2<\/sup>-4x+x -10 -18), the x2<\/sup> is the only exponent.\u00a0 Then, -4x +x equals -3x, for the variables.\u00a0 Then, (-10 -18) equals -28, so the numerator is now (x2<\/sup>-3x-28), which can be factored as (x +4)(x-7).\u00a0 Using FOIL to check, x\u00b7x equals x2<\/sup>, 4x-7x equals -3x, and (-7\u00b74) equals -28.\u00a0 The numerator [(x +4)(x-7)] can now be placed over the common denominator (x-7).\u00a0 The (x-7) in the numerator and denominator cancel out, so the answer in simplest terms is (x +4).<\/p>\n

Subtraction with Like Denominators<\/strong><\/h3>\n

As subtraction is adding the inverse, the process is very similar to addition of rational expressions with like denominators.\u00a0 The numerator is subtracted, then the rational expression is simplified.\u00a0 For example, \u00a0the first step to solve[(4m +5)\/(m-1)] \u2013 [(2m-1)\/(m-1)] is to combine the numerators as [(4m +5) \u2013(2m -1)] or 4m-2m +5 +1 or 2m +6.\u00a0 The expression 2m +6 is not in simplest terms, as it can be factored as 2(m +3).\u00a0 Then using the common denominator, the entire solution is [2(m +3)]\/(m-1).<\/p>\n

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Overview Adding and subtracting rational expressions with like denominators is similar to adding and subtracting fractions with like denominators.\u00a0 It is a three-step process: first add the numerators, then simplify the numerator, then simplify the result by factoring.\u00a0 Since subtraction is the inverse of addition, subtraction is a matter of adding the inverse of the […]<\/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":[4081,4083,4082],"class_list":["post-66936","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-adding-rational-expressions","tag-like-denominators","tag-subtracting-rational-expressions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66936","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=66936"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66936\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=66936"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=66936"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=66936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}