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

$\displaystyle \frac{x}{x+3}$
Simplifying Rational Expressions 1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator by any common factors. --- Numerator $:$ factor out x... $x(x^{2}-3x+9)=$ ... and, this is as far as it goes (not a perfect square, can't find factors of 9 whose sum is -3) Denominator: Numerator $:$ recognize a sum of cubes $x^{3}+3^{3}=(x+3)(x^{2}-3x+9)$ Expression = $\displaystyle \frac{x(x^{2}-3x+9)}{(x+3)(x^{2}-3x+9)}$ ... divide both with the common factor: $(x^{2}-3x+9)$ Expression = $\displaystyle \frac{x}{x+3}$