Answer
$3$
Work Step by Step
Re-arrange the given equation as follows; $\lim\limits_{(x,y) \to (1,-1)}\dfrac{(x^3-y^3)}{(x+y)}=\lim\limits_{(x,y) \to (1,-1)}\dfrac{(x+y)(x^2-xy+y^2)}{(x+y)}$
$\lim\limits_{(x,y) \to (1,-1)}\dfrac{(x+y)(x^2-xy+y^2)}{(x+y)}=\lim\limits_{(x,y) \to (1,-1)}(x^2-xy+y^2)$
Thus, $\lim\limits_{(x,y) \to (1,-1)}(x^2-xy+y^2)=1-(1)(-1)+(-1)^2=3$
