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: 37

Answer

$\dfrac{3x}{10}$

Work Step by Step

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