Answer
$-\displaystyle \frac{1}{a+b},\quad x\neq y$
Work Step by Step
To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
= $\displaystyle \frac{y-x}{ax+bx-ay-by}$
... factor the denominator in pairs,
... $ax+bx-ay-by=x(a+b)-y(a+b)=(a+b)(x-y)$
... also, we factor out -1 in the numerator to get common factors
$=\displaystyle \frac{-(x-y)}{(a+b)(x-y)}$
... common factors cancel,
... exclude the possibility that $x-y=0.$
= $-\displaystyle \frac{1}{a+b},\quad x\neq y$