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: 36

Answer

$\dfrac{4m}{3m^{2}+7m-6}-\dfrac{m}{3m^{2}-14m+8}=\dfrac{m(3m-19)}{(3m-2)(m+3)(m-4)}$

Work Step by Step

$\dfrac{4m}{3m^{2}+7m-6}-\dfrac{m}{3m^{2}-14m+8}$ Factor the denominators of both rational expressions: $\dfrac{4m}{3m^{2}+7m-6}-\dfrac{m}{3m^{2}-14m+8}=...$ $...=\dfrac{4m}{(m+3)(3m-2)}-\dfrac{m}{(3m-2)(m-4)}=...$ Evaluate the subtraction of the two rational expressions using the LCD, which is $(3m-2)(m+3)(m-4)$ in this case: $...=\dfrac{4m(m-4)-m(m+3)}{(3m-2)(m+3)(m-4)}=...$ Simplify: $...=\dfrac{4m^{2}-16m-m^{2}-3m}{(3m-2)(m+3)(m-4)}=...$ $...=\dfrac{3m^{2}-19m}{(3m-2)(m+3)(m-4)}=\dfrac{m(3m-19)}{(3m-2)(m+3)(m-4)}$
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