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: 21


$\displaystyle \frac{2}{x+2}$

Work Step by Step

To add rational expressions with the same denominator, add numerators and place the sum over the common denominator. If possible, factor and simplify the result. --- $\displaystyle \frac{x^{2}-2}{x^{2}+x-2}+\frac{2x-x^{2}}{x^{2}+x-2} = \displaystyle \frac{x^{2}-2+2x-x^{2}}{x^{2}+x-2}$ $= \displaystyle \frac{2x-2}{x^{2}+x-2}$ ... to factor the denominator, search for ... two factors of -2 whose sum is +1 ... we find +2 and -1 $= \displaystyle \frac{2(x-1)}{(x+2)(x-1)}\qquad$... reduce the common factors $=\displaystyle \frac{2}{x+2}$
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