Answer
$\displaystyle \frac{3x+1}{3x-4}$
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.
$\displaystyle \frac{5x-2}{3x-4}+\frac{2x-3}{4-3x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{5x-2}{3x-4}+ \frac{-2x+3}{3x-4}$
... 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.
$= \displaystyle \frac{5x-2-2x+3}{3x-4}$
$= \displaystyle \frac{3x+1}{3x-4}$