## College Algebra (10th Edition)

Published by Pearson

# Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 71: 61

#### Answer

LCM =$x(x-1)^{2}(x+1)(x^{2}+x+1)$

#### Work Step by Step

Step 1: Factor each polynomial completely. $x^{3}-x=x(x^{2}-1)=$ ... recognize a difference of squares $=x(x-1)(x+1)$ $x^{3}-2x^{2}+x=x(x^{2}-2x+1)$ ... recognize perfect square $=x(x-1)^{2}$ $x^{3}-1=\qquad$... a difference of cubes, $=(x-1)(x^{2}+x+1)$ 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 =$x(x-1)^{2}(x+1)(x^{2}+x+1)$

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