Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 45

Answer

$\dfrac{5x-20}{3x^{2}+x}\cdot\dfrac{3x^{2}+13x+4}{x^{2}-16}=\dfrac{5}{x}$

Work Step by Step

$\dfrac{5x-20}{3x^{2}+x}\cdot\dfrac{3x^{2}+13x+4}{x^{2}-16}$ Factor both rational expressions completely: $\dfrac{5x-20}{3x^{2}+x}\cdot\dfrac{3x^{2}+13x+4}{x^{2}-16}=\dfrac{5(x-4)}{x(3x+1)}\cdot\dfrac{(x+4)(3x+1)}{(x+4)(x-4)}=...$ Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{5(x-4)(x+4)(3x+1)}{x(x+4)(x-4)(3x+1)}=\dfrac{5}{x}$
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