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: 24

Answer

$y+6$

Work Step by Step

Adding the numerators and copying the denominator, the given expression, $ \dfrac{y^2+6y}{y+2}+\dfrac{2y+12}{y+2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{y^2+6y+2y+12}{y+2} \\\\= \dfrac{y^2+8y+12}{y+2} \\\\= \dfrac{(y+6)(y+2)}{y+2} \\\\= \dfrac{(y+6)(\cancel{y+2})}{\cancel{y+2}} \\\\= y+6 .\end{array}
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