Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.3 Rational Expressions - R.3 Exercises - Page R-11: 17


$\displaystyle \frac{1}{4}$

Work Step by Step

$\displaystyle \frac{2k-16}{6}\div\frac{4k-32}{3}=\qquad$ ... apply property:$ \displaystyle \frac{P}{Q}\div\frac{R}{S}=\frac{P}{Q}\cdot\frac{S}{R} $ $=\displaystyle \frac{2k-16}{6}\cdot\frac{3}{4k-32}$ ... factor out 2 in the first numerator, ... factor out 4 in the second denominator $=\displaystyle \frac{2(k-8)}{6}\cdot\frac{3}{4(k-8)}= \qquad$ ... apply property: $\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS}$ $=\displaystyle \frac{2\cdot 3(k-8)}{2\cdot 3\cdot 4(k-8)}\qquad$... reduce: 2, 3, $(k-8)$ $=\displaystyle \frac{1}{4}$
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