College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 71: 71


$\displaystyle \frac{x^{3}-2x^{2}+4x+3}{x^{2}(x+1)(x-1)}$

Work Step by Step

Step 1: Factor each denominator $x^{2}+x=x(x+1)$ $x^{3}-x^{2}=x^{2}(x-1)$ Step 2: The LCM is the product of each of these factors raised to a power equal to the greatest number of times that the factor occurs in the polynomials. LCM = $x^{2}(x+1)(x-1)$ Step 3: Write each rational expression using the LCM as the denominator. Simplify. $\displaystyle \frac{1\cdot x(x+1)(x-1)}{x\cdot x(x+1)(x-1)}-\frac{2\cdot x(x-1)}{x\cdot x(x+1)(x-1)}+\frac{3(x+1)}{x^{2}(x-1)(x+1)}$ $=\displaystyle \frac{x(x^{2}-1)-(2x^{2}-2x)+3x+3}{x^{2}(x+1)(x-1)}$ $=\displaystyle \frac{x^{3}-x-2x^{2}+2x+3x+3}{x^{2}(x+1)(x-1)}$ $=\displaystyle \frac{x^{3}-2x^{2}+4x+3}{x^{2}(x+1)(x-1)}$
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