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: 78

Answer

$\dfrac{8}{x^{2}+6x+5}-\dfrac{3x}{x^{2}+4x-5}+\dfrac{2}{x^{2}-1}=-\dfrac{3x^{2}-7x-2}{(x+5)(x+1)(x-1)}$

Work Step by Step

$\dfrac{8}{x^{2}+6x+5}-\dfrac{3x}{x^{2}+4x-5}+\dfrac{2}{x^{2}-1}$ Factor the three rational expressions completely: $\dfrac{8}{(x+5)(x+1)}-\dfrac{3x}{(x+5)(x-1)}+\dfrac{2}{(x-1)(x+1)}=...$ Evaluate the indicated operations and simplify: $...=\dfrac{8(x-1)-3x(x+1)+2(x+5)}{(x+5)(x+1)(x-1)}=...$ $...=\dfrac{8x-8-3x^{2}-3x+2x+10}{(x+5)(x+1)(x-1)}=\dfrac{-3x^{2}+7x+2}{(x+5)(x+1)(x-1)}=...$ $...=-\dfrac{3x^{2}-7x-2}{(x+5)(x+1)(x-1)}$
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