Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 56

Answer

$\dfrac{27}{y^{2}-81}+\dfrac{3}{2(y+9)}=\dfrac{3}{2(y-9)}$

Work Step by Step

$\dfrac{27}{y^{2}-81}+\dfrac{3}{2(y+9)}$ Factor the denominator of the first fraction: $\dfrac{27}{y^{2}-81}+\dfrac{3}{2(y+9)}=\dfrac{27}{(y-9)(y+9)}+\dfrac{3}{2(y+9)}=...$ Evaluate the sum of the two rational expressions and simplify: $...=\dfrac{27(2)+3(y-9)}{2(y+9)(y-9)}=\dfrac{54+3y-27}{2(y+9)(y-9)}=...$ $...=\dfrac{3y+27}{2(y+9)(y-9)}=...$ Take out common factor $3$ from the numerator to provide a more simplified answer: $...=\dfrac{3(y+9)}{2(y+9)(y-9)}=\dfrac{3}{2(y-9)}$
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