Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 8 Rational Functions - 8.5 Add and Subtract Rational Expressions - 8.5 Exercises - Skill Practice - Page 587: 39

Answer

See below

Work Step by Step

$$\frac{\frac{3-2x}{x^3}}{\frac{2}{x^2}-\frac{1}{x^3+x^2}}\\ =\frac{\frac{3-2x}{x^3}}{\frac{2}{x^2}-\frac{1}{x^2(x+1)}}$$ Multiply all terms by $x^3(x+1)$ $$\frac{\frac{3-2x}{x^3}}{\frac{2}{x^2}-\frac{1}{x^2(x+1)}}\\=\frac{\frac{3-2x}{x^3}}{\frac{2}{x^2}-\frac{1}{x^2(x+1)}}.\frac{x^3(x+1)}{x^3(x+1)}\\=\frac{(3-2x)(x+1)}{2x(x+1)-x}\\=-\frac{(2x-3)(x+1)}{x(2x+1)}$$
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