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: 29


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

Work Step by Step

We apply Method 1 (A51), to treat the numerator and denominator of the complex rational expression separately. So by factoring both the denominator and numerator of each rational function and cancelling the common factors, we have $$ \frac{\frac{4-x}{4+x}}{\frac{4x}{x^2-16}}=\frac{\frac{4-x}{4+x}}{\frac{4x}{(x+4)(x-4)}}= \frac{4-x}{4+x}\frac{(x+4)(x-4)}{4x}\\ =-\frac{(x-4)^2}{4x} .$$
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