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: 73


$\displaystyle \frac{-1}{x(x+h)}$

Work Step by Step

First, simplify $\displaystyle \frac{1}{x+h}-\frac{1}{x}$ LCD = $x(x+h)$ $\displaystyle \frac{1}{x+h}\cdot\frac{x}{x}-\frac{1}{x}\cdot\frac{x+h}{x+h}=\frac{x-(x+h)}{x(x+h)}$ $=\displaystyle \frac{-h}{x(x+h)}$ Now, $\displaystyle \frac{1}{h}\left(\frac{1}{x+h}-\frac{1}{x}\right)$=$\displaystyle \frac{1}{h}\left(\frac{-h}{x(x+h)}\right)$ ... h cancels, $=\displaystyle \frac{-1}{x(x+h)}$
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