Answer
The limit does not exist
Work Step by Step
Consider $f(x,y)=\dfrac{x-y}{x+y}$
Let us consider the approach: $(x,y) \to (0,0)$ along $y=mx; m\ne -10$
Then, we get $\lim\limits_{x \to 0} \dfrac{x-mx}{x+mx}=\dfrac{1-m}{1+m}$
This shows that there are multiple limit values when the approach is different and therefore, the limit does not exist for the given function.