Answer
$\displaystyle \frac{2}{x-3}$
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.
$\displaystyle \frac{4}{x-3}+\frac{2}{3-x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{4}{x-3}+\frac{-2}{x-3} = \displaystyle \frac{4}{x-3}-\frac{2}{x-3}$
... 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.
$= \displaystyle \frac{4-2}{x-3}$
$= \displaystyle \frac{2}{x-3}$
