College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 71: 53


$\displaystyle \frac{2(x^{2}-2)}{x(x+2)(x-2)}$

Work Step by Step

Factor the first denominator $x^{2}-4 =x^{2}-2^{2}=(x+2)(x-2).$ LCD = $x(x+2)(x-2)$ $\displaystyle \frac{x}{x^{2}-4}+\frac{1}{x}=\frac{x}{(x+2)(x-2)}+\frac{1}{x}$ $=\displaystyle \frac{x\cdot x+1\cdot(x+2)(x-2)}{x(x+2)(x-2)}$ $=\displaystyle \frac{x^{2}+(x^{2}-4)}{x(x+2)(x-2)}$ $=\displaystyle \frac{2x^{2}-4}{x(x+2)(x-2)}$ $=\displaystyle \frac{2(x^{2}-2)}{x(x+2)(x-2)}$
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