Answer
$\displaystyle \frac{3x+7}{x-6}$
Work Step by Step
.... 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.
$= \displaystyle \frac{6x+7-3x}{x-6}$
$= \displaystyle \frac{3x+7}{x-6}$
