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 493: 108


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

Work Step by Step

In order to simplify, we have to 1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator by any common factors. Factoring $x^{2}-x-6$, we search for two factors of -6 whose sum is -1... ... these are $-3$ and $+2$ . $x^{2}-x-6=(x-3)(x+2)$ Placing $(x+2)$ in the denominator, we will be able to divide both the numerator and the denominator by $(x+2)$. What remains is $=(x-3)$ $\displaystyle \frac{x^{2}-x-6}{x+2}=\frac{(x-3)(x+2)}{(x+2)}=\frac{x-3}{1}=x-3$
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