Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set: 21

Answer

$y-7$

Work Step by Step

When subtracting two fractions with common denominators, we subtract the numerators and copy the denominator. Therefore, the given expression, $ \dfrac{y^2}{y+2}-\dfrac{5y+14}{y+2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{y^2-(5y+14)}{y+2} \\\\= \dfrac{y^2-5y-14}{y+2} \\\\= \dfrac{(y-7)(y+2)}{y+2} \\\\= \dfrac{(y-7)(\cancel{y+2})}{\cancel{y+2}2} \\\\= y-7 .\end{array}
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