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: 29


$\displaystyle \frac{4}{5x(x-1)}$

Work Step by Step

$...=\displaystyle \frac{8x}{x^{2}-1}\div\frac{10x}{x+1}=\frac{8x}{x^{2}-1}\cdot\frac{x+1}{10x}$ Factoring, $8=4\cdot 2$ $10=5\cdot 2$ $ x^{2}-1=(x+1)(x-1)\quad$ (a difference of squares) $x^{2}=x\cdot x$ ... = $\displaystyle \frac{4\cdot 2\cdot x\cdot(x+1)}{(x+1)(x-1)\cdot 5\cdot 2\cdot x\cdot x}$ ... cancel the following from both sides of the fraction line: $2,\ x$, $(x+1)$ ... = $\displaystyle \frac{4}{5x(x-1)}$
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