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

$\displaystyle \frac{3x+7}{x-6}$
.... When one denominator is the opposite, or additive inverse of the other, first multiply either rational expression by $\displaystyle \frac{-1}{-1}$ to obtain a common denominator. $\displaystyle \frac{6x+7}{x-6}+\frac{3x}{6-x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{6x+7}{x-6}+ \frac{-3x}{x-6}$ $= \displaystyle \frac{6x+7}{x-6}- \frac{3x}{x-6}$ ... To add/subtract rational expressions with the same denominator, add/subtract numerators and place the sum/difference over the common denominator. If possible, factor and simplify the result. $= \displaystyle \frac{6x+7-3x}{x-6}$ $= \displaystyle \frac{3x+7}{x-6}$