{"id":66941,"date":"2017-11-19T20:37:46","date_gmt":"2017-11-19T20:37:46","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=66941"},"modified":"2017-11-19T20:37:46","modified_gmt":"2017-11-19T20:37:46","slug":"math-review-of-adding-rational-expressions-with-unlike-denominators","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-adding-rational-expressions-with-unlike-denominators\/","title":{"rendered":"Math Review of Adding Rational Expressions with Unlike Denominators"},"content":{"rendered":"

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

Adding rational expressions with unlike denominators is similar to adding fractions with unlike denominators.\u00a0 The first step is to find the least common multiple (LCM) of the denominators.\u00a0 This can then form the least common denominator.\u00a0 Then multiply each rational expression so that it has the least common denominator.\u00a0 Next, add the numerators now that the denominators are alike.\u00a0 They can be factored and simplified.\u00a0 Subtraction is the process of adding the inverse.<\/p>\n

Finding the Least Common Multiple<\/strong><\/h3>\n

To find the LCM of two or more algebraic expressions, first factor each expression.\u00a0 Then, multiply all of the factors.\u00a0 This is similar to finding the common factors of ordinary numbers without variables.\u00a0 For example, the number 6 can be factored as 2\u00b73, and the number 10 can be factored as 2\u00b75.\u00a0 Their least common multiple is 2\u00b73\u00b75 or 30.\u00a0 Compare that to just multiplying 6\u00b710, or 60.\u00a0 The process is similar with expressions containing variables.\u00a0 Suppose the expressions are 8x2<\/sup>y2<\/sup> and 12xy3<\/sup>.\u00a0 The coefficient 8 can be factored as 2\u00b72\u00b72 and the coefficient 12 can be factored as 2\u00b72\u00b73.\u00a0 The LCM of 8 and 12 can be factored as 2\u00b72\u00b72\u00b73 or 24.\u00a0 Similarly, the LCM of x2<\/sup> and x is x2<\/sup> and the LCM of y2<\/sup> and y3<\/sup> is y3<\/sup>.\u00a0 Putting them together, the LCM of 8x2<\/sup>y2<\/sup> and 12xy3<\/sup> is 24x2<\/sup>y3<\/sup>.<\/p>\n

<\/h3>\n

Factoring Expressions<\/strong><\/h3>\n

In order to find the LCM of polynomial expressions, it is also necessary to factor them first, if they can be factored.\u00a0 Suppose one expression is y2<\/sup> +5y +4 and the other is y2<\/sup> +2y +1.\u00a0 The first polynomial can be factored as (y +4) (y +1), and the second one can be factored as (y +1) (y +1).\u00a0 The LCM is (y +4) (y+1) (y +1), or (y +1)2<\/sup>(y +4).\u00a0 Expressions such as (t2<\/sup>+16) and (t-2) have no factors in common, so their LCM is (t2<\/sup>+16) (t-2).<\/p>\n

Addition with Unlike Denominators<\/strong><\/h3>\n

In order to add expressions with unlike denominators, first find the LCM of the denominators.\u00a0 This can be used to form their LCD.\u00a0 Then write each expression as an equivalent expression by multiplying it by a form of 1 using the LCD.\u00a0 The numerators can then be added, and the rational expression can be simplified.\u00a0 Suppose the expressions are (7x2<\/sup>)\/6 and (3x)\/16.\u00a0\u00a0\u00a0 First, find the LCM of 6 and 16.\u00a0 The number 6 factors as 2\u00b73 and the number 16 factors as 2\u00b72\u00b72\u00b72.\u00a0 Their LCM will be 2\u00b72\u00b72\u00b72\u00b73 or 48.\u00a0 The expression is [(7x2<\/sup>)\/6] \u00b78\/8, or (56x2<\/sup>)\/48 + [(3x)\/16] \u00b73\/3 or (9x)\/48.\u00a0 Adding expressions over like denominators, the solution is then (56x2<\/sup> +9x)\/48.<\/p>\n

<\/h3>\n

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

Subtraction with unlike denominators is similar to addition with unlike denominators, with an additional step. \u00a0First, find the LCM of the unlike denominators to form the LCD.\u00a0 Then write each expression as an equivalent expression by multiplying it by a form of 1 using the LCD.\u00a0 Then, subtract the numerators and write the difference over the LCD. The resulting rational expression can then be simplified.\u00a0 For example, the expression is [(y +2)\/(y-4)]-[(y +1)\/(y +4)].\u00a0 First, multiply [(y +2)\/(y-4)] by [(y+4)\/(y+4)].\u00a0 The numerator is then (y +2) (y +4).\u00a0 Then multiply – [(y +1)\/(y +4)] by [(y-4)\/(y-4).\u00a0 The numerator is then \u2013 [(y+1) (y-4)].\u00a0 Both are multiplied by the LCM, so the new numerator is {[(y +2) (y +4)] – [(y+1)(y-4)]}.\u00a0 Expanding the numerator, (y +2 )(y +4 equals y2<\/sup> +6y +8, and -[(y+1)(y-4)] equals \u2013(y2<\/sup>-3y-4) \u00a0or -y2<\/sup> +3y +4, or y2<\/sup>-y2<\/sup> +6y +3y+8 +4 or (9y +12)\/[(y +4)(y-4)] or 3(3y+4)\/[(y +4)(y-4)].<\/p>\n

<\/h3>\n

Interested in\u00a0math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.
\nSchoolTutoring Academy<\/a>\u00a0<\/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\u00a0Selma, AL: visit:\u00a0Tutoring in Selma, AL<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Adding rational expressions with unlike denominators is similar to adding fractions with unlike denominators.\u00a0 The first step is to find the least common multiple (LCM) of the denominators.\u00a0 This can then form the least common denominator.\u00a0 Then multiply each rational expression so that it has the least common denominator.\u00a0 Next, add the numerators now […]<\/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":[4084,4086,4087,4085],"class_list":["post-66941","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-addition-of-rational-expressions-with-unlike-denominators","tag-least-common-denominator-lcd","tag-least-common-multiple-lcm","tag-subtraction-of-rational-expressions-with-unlike-denominators"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/66941","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=66941"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/66941\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=66941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=66941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=66941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}