Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.5 - Rational Expressions - Exercises - Page 49: 60

Answer

$\frac{2+x^2}{x^3\sqrt{1-x^2}}$

Work Step by Step

$\frac{-x^3(1-x^2)^{-1/2}-2x(1-x^2)^{1/2}}{x^4}=\frac{-x^3(1-x^2)^{-1/2}(1-x^2)^{1/2}-2x(1-x^2)^{1/2}(1-x^2)^{1/2}}{x^4(1-x^2)^{1/2}}=\frac{-x^3-2x(1-x^2)}{x^4\sqrt{1-x^2}}=\frac{-x^3-2x+2x^3}{x^4\sqrt{1-x^2}}=\frac{2x+x^3}{x^4\sqrt{1-x^2}}=\frac{2+x^2}{x^3\sqrt{1-x^2}}$
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