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 72: 78


$\displaystyle \frac{x}{(x+1)^{2}}$

Work Step by Step

$\displaystyle \frac{1-\frac{x}{x+1}}{2-\frac{x-1}{x}}=(1-\frac{x}{x+1})\div(2-\frac{x-1}{x})$ $=(\displaystyle \frac{x+1}{x+1}-\frac{x}{x+1})\div(\frac{2x}{x}-\frac{x-1}{x})$ $=(\displaystyle \frac{1}{x+1})\div(\frac{x+1}{x})$ ... division = multiplication with the reciprocal, $=\displaystyle \frac{1}{x+1}\cdot\frac{x}{x+1}$ $=\displaystyle \frac{x}{(x+1)^{2}}$
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