Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 36



Work Step by Step

$\dfrac{\dfrac{2x^{2}-3x-2}{x^{2}-1}}{\dfrac{2x^{2}+5x+2}{x^{2}+x-2}}$ Factor the expression completely: $\dfrac{\dfrac{2x^{2}-3x-2}{x^{2}-1}}{\dfrac{2x^{2}+5x+2}{x^{2}+x-2}}=\dfrac{\dfrac{(x-2)(2x+1)}{(x+1)(x-1)}}{\dfrac{(2x+1)(x+2)}{(x-1)(x+2)}}=...$ Evaluate the division: $...=\dfrac{(x-2)(2x+1)(x-1)(x+2)}{(2x+1)(x+2)(x+1)(x-1)}=...$ Simplify: $...=\dfrac{x-2}{x+1}$
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