## Introductory Algebra for College Students (7th Edition)

$\displaystyle \frac{x+5}{x-5}$
Simplifying Rational Expressions 1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator by any common factors. --- Numerator: fully factored Denominator: recognize a difference of squares $x^{2}-5^{2}=(x+5)(x-5)$ Expression = $\displaystyle \frac{(x+5)^{2}}{(x+5)(x-5)}$ ... divide both with the common factor: $(x+5)$ Expression = $\displaystyle \frac{x+5}{x-5}$