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: 77


$\displaystyle \frac{x-6}{x^{2}+3x+9} $

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 $:$ search for integer factors of $+18$ whose sum is $-9$... ... these are $-3$ and $-6...$ $x^{2}-9x+18 =(x-3)(x-6)$ Denominator: recognize a difference of cubes $x^{3}-3^{3}=(x-3)(x^{2}+3x+9)$ Expression = $\displaystyle \frac{(x-3)(x-6)}{(x-3)(x^{2}+3x+9)}$ ... divide both with the common factor: $ (x-3)$ Expression = $\displaystyle \frac{x-6}{x^{2}+3x+9} $
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