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: 43

Answer

$\displaystyle \frac{3x+1}{3x-4}$

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. $\displaystyle \frac{5x-2}{3x-4}+\frac{2x-3}{4-3x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{5x-2}{3x-4}+ \frac{-2x+3}{3x-4}$ ... 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. $= \displaystyle \frac{5x-2-2x+3}{3x-4}$ $= \displaystyle \frac{3x+1}{3x-4}$
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