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: 19


$\dfrac{2x(x^2+4x+16)}{x+4} $

Work Step by Step

By factoring both the denominator and numerator of each rational function and cancelling the common factors, we have $$ \frac{4x^2}{x^2-16}\cdot \frac{x^3-64}{2x} = \frac{4x^2}{(x-4)(x+4)}\cdot \frac{(x-4)(x^2+4x+16)}{2x} \\ = \frac{2x(x^2+4x+16)}{x+4} .$$
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