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: 72


$ \displaystyle \frac{3x^{3}-5x^{2}+2x+1}{x^{2}(x-1)}$

Work Step by Step

Step 1: Factor each denominator The first two are already factored, $(x-1)^{2},\ x$ $x^{3}-x^{2}=x^{2}(x-1)$ 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 = $x^{2}(x-1)^{2}$ Step 3: Write each rational expression using the LCM as the denominator. Simplify. $\displaystyle \frac{x\cdot x^{2}}{(x-1)^{2}\cdot x^{2}}+\frac{2\cdot x(x-1)^{2}}{x\cdot x(x-1)^{2}}-\frac{(x+1)(x-1)}{x^{2}(x-1)(x-1)}$ $ = \displaystyle \frac{x^{3}+2x(x^{2}-2x+1)-(x^{2}-1)}{x^{2}(x-1)^2}$ $ = \displaystyle \frac{x^{3}+2x^{3}-4x^{2}+2x-x^{2}+1}{x^{2}(x-1)^2}$ $= \displaystyle \frac{3x^{3}-5x^{2}+2x+1}{x^{2}(x-1)^2}$
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