Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Review: 70

Answer

$\dfrac{3x}{x^{2}+9x+14}-\dfrac{6x}{x^{2}+4x-21}=-\dfrac{3x}{(x+2)(x-3)}$

Work Step by Step

$\dfrac{3x}{x^{2}+9x+14}-\dfrac{6x}{x^{2}+4x-21}$ Factor both denominators: $\dfrac{3x}{(x+7)(x+2)}-\dfrac{6x}{(x+7)(x-3)}=...$ Evaluate the substraction: $...=\dfrac{3x(x-3)-6x(x+2)}{(x+7)(x+2)(x-3)}=\dfrac{3x^{2}-9x-6x^{2}-12x}{(x+7)(x+2)(x-3)}=...$ $...=\dfrac{-3x^{2}-21x}{(x+7)(x+2)(x-3)}=...$ Take out common factor $-3x$ from the numerator and simplify: $...=\dfrac{-3x(x+7)}{(x+7)(x+2)(x-3)}=-\dfrac{3x}{(x+2)(x-3)}$
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