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: 31


$-\displaystyle \frac{(x-4)^{2}}{4x}$

Work Step by Step

$...=\displaystyle \frac{4-x}{4+x}\div\frac{4x}{x^{2}-16}=\frac{4-x}{4+x}\cdot\frac{x^{2}-16}{4x}$ Factoring, $ x^{2}-16=(x+4)(x-4)\quad$ (a difference of squares) $4-x=-(x-4)$ ... = $\displaystyle \frac{-(x-4)(x-4)(x+4)}{(x+4)\cdot 4x}$ ... cancel the following from both sides of the fraction line: $(x+4)$ ... = $-\displaystyle \frac{(x-4)(x-4)}{4x}$ = $-\displaystyle \frac{(x-4)^{2}}{4x}$
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