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: 70


$-\displaystyle \frac{1}{a+b},\quad x\neq y$

Work Step by Step

To add/subtract rational expressions with the same denominator, add/subtract numerators and place the sum/difference over the common denominator. = $\displaystyle \frac{y-x}{ax+bx-ay-by}$ ... factor the denominator in pairs, ... $ax+bx-ay-by=x(a+b)-y(a+b)=(a+b)(x-y)$ ... also, we factor out -1 in the numerator to get common factors $=\displaystyle \frac{-(x-y)}{(a+b)(x-y)}$ ... common factors cancel, ... exclude the possibility that $x-y=0.$ = $-\displaystyle \frac{1}{a+b},\quad x\neq y$
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