Answer
$0$
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.
$\displaystyle \frac{y-3}{y^{2}-25}+\frac{y-3}{25-y^{2}}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{y-3}{y^{2}-25}+ \frac{-y+3}{x-3}$
... 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.
$= \displaystyle \frac{y-3-y+3}{y^{2}-25}$
$= \displaystyle \frac{0}{y^{2}-25}$
$=0$