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: 23

Answer

$\dfrac{2m^{2}-5m-12}{m^{2}-10m+24}\div\dfrac{4m^{2}-9}{m^{2}-9m+18}=\dfrac{m-3}{2m-3}$

Work Step by Step

$\dfrac{2m^{2}-5m-12}{m^{2}-10m+24}\div\dfrac{4m^{2}-9}{m^{2}-9m+18}$ Factor both rational expressions completely: $\dfrac{2m^{2}-5m-12}{m^{2}-10m+24}\div\dfrac{4m^{2}-9}{m^{2}-9m+18}=...$ $...=\dfrac{(2m+3)(m-4)}{(m-6)(m-4)}\div\dfrac{(2m+3)(2m-3)}{(m-6)(m-3)}=...$ Evaluate the division of the two fractions: $...=\dfrac{(2m+3)(m-4)(m-6)(m-3)}{(m-6)(m-4)(2m+3)(2m-3)}=...$ Simplify by removing the factors that appear both in the numerator and in the denominator of the resulting rational expression: $...=\dfrac{m-3}{2m-3}$
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