Algebra: A Combined Approach (4th Edition)

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

Chapter 13 - Cumulative Review - Page 969: 30

Answer

$\frac{3x^{2}+7x-45}{(3x-2)(3x+2)(x-5)}$

Work Step by Step

We simplify as follows: $\frac{x}{3x^{2}-13x-10}+\frac{9}{9x^{2}-4}$ $=\frac{x}{(3x+2)(x-5)}+\frac{9}{(3x-2)(3x+2)}$ $=\frac{x(3x-2)}{(3x-2)(3x+2)(x-5)}+\frac{9(x-5)}{(3x-2)(3x+2)(x-5)}$ $=\frac{x(3x-2)+9(x-5)}{(3x-2)(3x+2)(x-5)}$ $=\frac{3x^{2}+7x-45}{(3x-2)(3x+2)(x-5)}$
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