Calculus 8th Edition

$-2/3$
Factoring out $x+y$ $$\lim\limits_{(x,y) \to (2,-1)} \frac{xy(x+y)}{(x+y)(x-y)}= \lim\limits_{(x,y) \to (2,-1)} \frac{xy}{(x-y)} = \frac{2*-1}{2+1}=-2/3$$