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: 84


$\displaystyle \frac{x}{x+3}$

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 x... $x(x^{2}-3x+9)=$ ... and, this is as far as it goes (not a perfect square, can't find factors of 9 whose sum is -3) Denominator: Numerator $:$ recognize a sum of cubes $x^{3}+3^{3}=(x+3)(x^{2}-3x+9)$ Expression = $\displaystyle \frac{x(x^{2}-3x+9)}{(x+3)(x^{2}-3x+9)}$ ... divide both with the common factor: $(x^{2}-3x+9)$ Expression = $\displaystyle \frac{x}{x+3}$
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