Answer
$\dfrac{1}{2}$
Work Step by Step
We need to find the limit for $\lim\limits_{(x,y) \to (1,1)} \dfrac{x-y}{x^2-y^2}$
or, $\lim\limits_{(x,y) \to (1,1)} \dfrac{x-y}{x^2-y^2}=\lim\limits_{(x,y) \to (1,1)} \dfrac{x-y}{(x-y)(x+y)}=\lim\limits_{(x,y) \to (1,1)} \dfrac{1}{x+y}$
Thus, $\dfrac{1}{1+1}=\dfrac{1}{2}$