Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.4 The Algebra of Functions - 7.4 Exercise Set: 34

Answer

$\dfrac{10}{3x}$

Work Step by Step

RECALL: $(f/g)(x) = \dfrac{f(x)}{g(x)}$ Using the formula above gives: $(r/t)(x) \\= \dfrac{r(x)}{t(x)} \\=\dfrac{\frac{5}{x^2}}{\frac{3}{2x}}$ Use the rule $\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{a}{b} \times \dfrac{d}{c}$ to obtain: $\require{cancel} \\=\dfrac{5}{x^2} \cdot \dfrac{2x}{3} \\=\dfrac{5}{\cancel{x^2}x} \cdot \dfrac{2\cancel{x}}{3} \\=\dfrac{10}{3x}$
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