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: 41

Answer

$\dfrac{7}{(x+1)(x-1)}+\dfrac{8}{(x+1)^{2}}=\dfrac{15x-1}{(x+1)^{2}(x-1)}$

Work Step by Step

$\dfrac{7}{(x+1)(x-1)}+\dfrac{8}{(x+1)^{2}}$ Evaluate the sum of the two rational expressions: $\dfrac{7}{(x+1)(x-1)}+\dfrac{8}{(x+1)^{2}}=\dfrac{7(x+1)^{2}+8(x+1)(x-1)}{(x+1)^{3}(x-1)}=...$ Take out common factor $x+1$ from the numerator and simplify: $...=\dfrac{(x+1)[7(x+1)+8(x-1)]}{(x+1)^{3}(x-1)}=\dfrac{7(x+1)+8(x-1)}{(x+1)^{2}(x-1)}=...$ $...=\dfrac{7x+7+8x-8}{(x+1)^{2}(x-1)}=\dfrac{15x-1}{(x+1)^{2}(x-1)}$
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