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: 52


$\displaystyle \frac{x^{2}+5x+25}{x+5} $

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: $x^{3}-5^{3}=(x-5)(x^{2}+5x+25)$ Denominator: recognize a difference of squares $x^{2}-5^{2}=(x+5)(x-5)$ Expression = $\displaystyle \frac{(x-5)(x^{2}+5x+25)}{(x+5)(x-5)}$ ... divide both with the common factor: $(x-5)$ Expression = $\displaystyle \frac{x^{2}+5x+25}{x+5} $
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