Explanation Given Information: The rational expression is 4 y y 2 − 1 − 5 y 2 + 2 y + 1 . Formula used: Subtracting Rational Expressions (Different Denominator). There are following steps to add the rational expressions with different denominators. Step 1: The least common denominator (LCD). Step 2: Simplify each rational expression in the form of an equivalent rational expression with the LCD as the denominator. Step 3: Obtain the numerator of the sum by adding the numerators where the LCD is the denominator of the sum. Step 4: Calculate the lowest terms by using the fundamental property. Calculation: Consider the rational expression. 4 y y 2 − 1 − 5 y 2 + 2 y + 1 Factorise the expressions in the denominators. y 2 − 1 = ( y − 1 ) ( y + 1 ) And y 2 + 2 y + 1 = ( y + 1 ) ( y + 1 ) So, the rational expression becomes, 4 y ( y − 1 ) ( y + 1 ) − 5 ( y + 1 ) ( y + 1 ) The LCD of ( y − 1 ) ( y + 1 ) and ( y + 1 ) ( y + 1 ) is ( y + 1 ) ( y + 1 ) ( y − 1 ) . Each rational expression as a fraction with the LCD as the denominator. The LCD is ( y + 1 ) ( y + 1 ) ( y − 1 ) . 4 y ( y − 1 ) ( y + 1 ) − 5 ( y + 1 ) ( y + 1 ) = ( 4 y ) ( y + 1 ) ( y − 1 ) ( y + 1 ) ( y + 1 ) − ( 5 ) ( y − 1 ) ( y + 1 ) ( y + 1 ) ( y − 1 ) Since, the fractions have the common denominator, subtract the numerators and the LCD is the denominator

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 6.4, Problem 49E

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To calculate: The value of 4yy2−1−5y2+2y+1 in the lowest term.

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Chapter 6.4, Problem 48E

Chapter 6.4, Problem 50E

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Chapter 6 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Concept Check Work each problem. Which two of the...Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The value of 4 y y 2 − 1 − 5 y 2 + 2 y + 1 in the lowest term.

Solution Summary: The author explains how to add rational expressions with different denominators.

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