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: 30

Answer

$\dfrac{y-5}{y+4}$

Work Step by Step

Adding the numerators and copying the denominator, the given expression, $ \dfrac{y^2-7y}{y^2+8y+16}+\dfrac{6y-20}{y^2+8y+16} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{y^2-7y+6y-20}{y^2+8y+16} \\\\= \dfrac{y^2-y-20}{y^2+8y+16} \\\\= \dfrac{(y-5)(y+4)}{(y+4)(y+4)} \\\\= \dfrac{(y-5)(\cancel{y+4})}{(y+4)(\cancel{y+4})} \\\\= \dfrac{y-5}{y+4} .\end{array}
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