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: 20

Answer

$\dfrac{6r-18}{9r^{2}+6r-24}\cdot\dfrac{12r-16}{4r-12}=\dfrac{2}{r+2}$

Work Step by Step

$\dfrac{6r-18}{9r^{2}+6r-24}\cdot\dfrac{12r-16}{4r-12}$ Factor both rational expressions completely: $\dfrac{6r-18}{9r^{2}+6r-24}\cdot\dfrac{12r-16}{4r-12}=\dfrac{6(r-3)}{3(r+2)(3r-4)}\cdot\dfrac{4(3r-4)}{4(r-3)}=...$ Evaluate the product of the two fractions: $...=\dfrac{(6)(4)(r-3)(3r-4)}{(3)(4)(r+2)(3r-4)(r-3)}=...$ Simplify by removing the factors that appear both in the numerator and in the denominator of the resulting expression: $...=\dfrac{6}{3(r+2)}=\dfrac{2}{r+2}$
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