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: 44



Work Step by Step

Since the numerator consists of a trinomial, we use the rules of factoring trinomials in order to factor it. For the factoring of the denominator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{x^{2}-3xy+2y^{2}}{x^{2}-4y^{2}}$ =$\frac{x^{2}-1xy-2xy+2y^{2}}{x^{2}-(2y)^{2}}$ =$\frac{x(x-y)-2y(x-y)}{(x+2y)(x-2y)}$ =$\frac{(x-y)(x-2y)}{(x+2y)(x-2y)}$ =$\frac{(x-y)}{(x+2y)}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.