Answer
$\displaystyle \frac{2(y-7)}{(y-5)(y+5)}$
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.
$\displaystyle \frac{y-7}{y^{2}-16}+\frac{7-y}{16-y^{2}} \cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{y-7}{y^{2}-16}+ \frac{-7+y}{y^{2}-16}$
... 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.
$= \displaystyle \frac{y-7-7+y}{y^{2}-16}$
$= \displaystyle \frac{2y-14}{y^{2}-25}$
... recognize a difference of squares in the denominator
$= \displaystyle \frac{2(y-7)}{(y-5)(y+5)}$
... no common factors to reduce the expression
