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: 57


$\displaystyle \frac{2x-4}{x^{2}-25}$

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. $\displaystyle \frac{x-2}{x^{2}-25}-\frac{x-2}{25-x^{2}} \cdot \displaystyle \frac{-1}{-1}=\frac{x-2}{x^{2}-25}-\frac{-(x-2)}{-(25-x^{2})}$ $=\displaystyle \frac{x-2}{x^{2}-25}-\frac{-(x-2)}{x^{2}-25} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$ $=\displaystyle \frac{x-2}{x^{2}-25}+\frac{(x-2)}{x^{2}-25}$ ... To add/subtract rational expressions with the same denominator, add/subtract numerators and place the sum/difference over the common denominator. $=\displaystyle \frac{x-2+x-2}{x^{2}-25}$ = $\displaystyle \frac{2x-4}{x^{2}-25}$
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