Answer
$\displaystyle \frac{2x+5}{x-2}$
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.
$\displaystyle \frac{6x+5}{x-2}+\frac{4x}{2-x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{6x+5}{x-2}+ \frac{-4x}{x-2}$
$= \displaystyle \frac{6x+5}{x-2}- \frac{4x}{x-2}$
... 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.
$= \displaystyle \frac{6x+5-4x}{x-2}$
$= \displaystyle \frac{2x+5}{x-2}$
