Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 84: 24


$= \displaystyle \frac{9}{28},\qquad x\neq-5$

Work Step by Step

Factor what we can: $\displaystyle \frac{x+5}{7}\div\frac{4x+20}{9}=\frac{x+5}{7}\div\frac{4(x+5)}{9}$ Division with $\displaystyle \frac{a}{b}$ equals multiplication with $\displaystyle \frac{b}{a}.$ (neither a or b can be 0) $=\displaystyle \frac{(x+5)}{7}\cdot\frac{9}{4(x+5)}$ ...exclude the values that yield 0 in the denominator: $x\neq-5$ ... cancel common factors $= \displaystyle \frac{9}{28},\qquad x\neq-5$
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