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: 26


$\dfrac{3(x-4)}{5x} $

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 $$ \frac{\frac{12x}{5x+20}}{\frac{4x^2}{x^2-16}}= \frac{\frac{12x}{5(x+4)}}{\frac{4x^2}{(x+4)(x-4)}}= \frac{12x}{5(x+4)}\frac{(x+4)(x-4)}{4x^2}\\ =\frac{3(x-4)}{5x} .$$
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