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: 22

Answer

$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}=\dfrac{m+6}{m+3}$

Work Step by Step

$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}$ Factor both rational expressions completely: $\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}=...$ $...=\dfrac{(m+2)(m+1)}{(m+4)(m+1)}\div\dfrac{(m+3)(m+2)}{(m+6)(m+4)}=...$ Evaluate the division of the two rational expressions: $...=\dfrac{(m+2)(m+1)(m+6)(m+4)}{(m+4)(m+1)(m+3)(m+2)}=...$ Simplify the resulting expression by removing the factors that appear both in the numerator and in the denominator: $...=\dfrac{m+6}{m+3}$
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