Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Section 7.1 - Rational Expressions and Their Simplification - Exercise Set - Page 492: 83


$\displaystyle \frac{2}{1-2x}$

Work Step by Step

Simplifying Rational Expressions 1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator by any common factors. --- Numerator $:$ factor out 2... $2(4x^{2}+2x+1)=$ ... and, this is as far as it goes (not a perfect square, can't find factors of 4 that add up to 2) Denominator: Numerator $:$ recognize a difference of cubes $1^{3}-(2x)^{3}=(1-2x)(4x^{2}+2x+1)$ Expression = $\displaystyle \frac{2(4x^{2}+2x+1)}{(1-2x(4x^{2}+2x+1)}$ ... divide both with the common factor: $(4x^{2}+2x+1)$ Expression = $\displaystyle \frac{2}{1-2x}$
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