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

$\displaystyle \frac{x-2}{x-3}$
To add rational expressions with the same denominator, add numerators and place the sum over the common denominator. If possible, factor and simplify the result. --- $\displaystyle \frac{x^{2}-4x}{x^{2}-x-6}+\frac{4x-4}{x^{2}-x-6} = \displaystyle \frac{x^{2}-4x+4x-4}{x^{2}-x-6}$ $= \displaystyle \frac{x^{2}-4}{x^{2}-x-6}$ ... Numerator: a difference of squares, ... To factor the denominator, search for ... two factors of -6 whose sum is -1. ... We find +2 and -3 $= \displaystyle \frac{(x+2)(x-2)}{(x+2)(x-3)}\qquad$... reduce the common factors $=\displaystyle \frac{x-2}{x-3}$