College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 36

Answer

$\frac{x-2}{x+1}$

Work Step by Step

We switch from division to multiplication by taking the reciprocal of the bottom fraction. Then we factor and simplify: $\displaystyle\frac{\frac{2x^{2}-3x-2}{x^2-1}}{\frac{2x^{2}+5x+2}{x^2+x-2}}=\frac{2x^{2}-3x-2}{x^{2}-1}*\frac{x^{2}+x-2}{2x^{2}+5x+2}=\frac{(x-2)(2x+1)}{(x-1)(x+1)}*\frac{(x-1)(x+2)}{(x+2)(2x+1)}=\frac{x-2}{x+1}$
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