Answer
$\displaystyle \frac{1}{x-6}$ , $\; x\neq-5$
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.
$\displaystyle \frac{2x+3}{x^{2}-x-30}+\frac{x-2}{30+x-x^{2}} \cdot \displaystyle \frac{-1}{-1}= \displaystyle \frac{2x+3}{x^{2}-x-30}+\frac{-(x-2)}{-(30+x-x^{2})}$
$= \displaystyle \frac{2x+3}{x^{2}-x-30}+\frac{-x+2}{x^{2}-x-30} $
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$= \displaystyle \frac{x+5}{x^{2}-x-30}$
... factor what you can
... for trinomials $x^{2}+bx+c$... find factors of $c$ whose sum is $b$
$=\displaystyle \frac{(x+5)}{(x+5)(x-6)}$
... common factors cancel,
= $\displaystyle \frac{1}{x-6}$ , $\; x\neq-5$
