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: 19

Answer

$\dfrac{4a+12}{2a-10}\div\dfrac{a^{2}-9}{a^{2}-a-20}=\dfrac{2(a+4)}{a-3}$

Work Step by Step

$\dfrac{4a+12}{2a-10}\div\dfrac{a^{2}-9}{a^{2}-a-20}$ Factor both rational expressions completely: $\dfrac{4a+12}{2a-10}\div\dfrac{a^{2}-9}{a^{2}-a-20}=\dfrac{4(a+3)}{2(a-5)}\div\dfrac{(a-3)(a+3)}{(a-5)(a+4)}=...$ Evaluate the division of the two fractions: $...=\dfrac{4(a+3)(a-5)(a+4)}{2(a-5)(a-3)(a+3)}=...$ Simplify by removing the factors that appear both in the numerator and in the denominator: $...=\dfrac{4(a+4)}{2(a-3)}=\dfrac{2(a+4)}{a-3}$
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