Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 38



Work Step by Step

$\dfrac{3}{x^{2}+2x-8}+\dfrac{2}{x^{2}-3x+2}$ Factor both denominators: $\dfrac{3}{(x+4)(x-2)}+\dfrac{2}{(x-2)(x-1)}=...$ Evaluate the sum: $...=\dfrac{3(x-1)+2(x+4)}{(x+4)(x-2)(x-1)}=\dfrac{3x-3+2x+8}{(x+4)(x-2)(x-1)}=...$ $...=\dfrac{5x+5}{(x+4)(x-2)(x-1)}=...$ Take out common factor $5$ to provide a more simplified answer: $...=\dfrac{5(x+1)}{(x+4)(x-2)(x-1)}$
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