Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.6 Rational Expressions - A.6 Assess Your Understanding - Page A53: 46



Work Step by Step

Since the least common multiple (LCM) of the denominator is $(x-5)(x+5)$, then we have $$ \frac{2}{x+5}-\frac{5}{x-5}=\frac{2(x-5)}{(x-5)(x+5)}-\frac{5(x+5)}{(x-5)(x+5)} .$$ Now, since the denominators are the same, then we have $$ \frac{2(x-5)}{(x-5)(x+5)}-\frac{5(x+5)}{(x-5)(x+5)}=\frac{2x-10-5x-25}{(x-5)(x+5)}\\ =\frac{-3x-35}{(x-5)(x+5)}=-\frac{3x+35}{(x-5)(x+5)} .$$
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