Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.1 - Simplifying Algebraic Fractions - Problem Set 7.1 - Page 281: 43



Work Step by Step

Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{x^{2}+2xy-3y^{2}}{2x^{2}-xy-y^{2}}$ =$\frac{x^{2}-1xy+3xy-3y^{2}}{2x^{2}+1xy-2xy-y^{2}}$ =$\frac{x(x-y)+3y(x-y)}{x(2x+y)-y(2x+y)}$ =$\frac{(x-y)(x+3y)}{(2x+y)(x-y)}$ =$\frac{(x+3y)}{(2x+y)}$
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