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: 78


$\displaystyle \frac{x^{2}+2x+4}{x+4}$

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 $:$ recognize a difference of cubes $x^{3}-2^{3}=(x-2)(x^{2}+2x+4)$ Denominator: search for integer factors of $-8$ whose sum is $+2$... ... these are $+4$ and $-2...$ $x^{2}+2x-8 =(x+4)(x-2)$ Expression = $\displaystyle \frac{(x-2)(x^{2}+2x+4)}{(x+4)(x-2)}$ ... divide both with the common factor: $ (x-2)$ Expression = $\displaystyle \frac{x^{2}+2x+4}{x+4}$
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