Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator - Exercise Set - Page 507: 41


$\displaystyle \frac{3x+7}{x-6}$

Work Step by Step

.... When one denominator is the opposite, or additive inverse of the other, first multiply either rational expression by $\displaystyle \frac{-1}{-1}$ to obtain a common denominator. $\displaystyle \frac{6x+7}{x-6}+\frac{3x}{6-x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{6x+7}{x-6}+ \frac{-3x}{x-6}$ $= \displaystyle \frac{6x+7}{x-6}- \frac{3x}{x-6}$ ... To add/subtract rational expressions with the same denominator, add/subtract numerators and place the sum/difference over the common denominator. If possible, factor and simplify the result. $= \displaystyle \frac{6x+7-3x}{x-6}$ $= \displaystyle \frac{3x+7}{x-6}$
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