Answer
$$\frac{3}{10}.$$
Work Step by Step
We are given $ \lim\limits_{(x,y) \to (2,5)}f(x,y)=3$ and $ \lim\limits_{(x,y) \to (2,5)}g(x,y)=7$, then we have
$$ \lim\limits_{(x,y) \to (2,5)}\frac{f(x,y)}{f(x,y)+g(x,y)}=\frac{ \lim\limits_{(x,y) \to (2,5)}f(x,y)}{ \lim\limits_{(x,y) \to (2,5)}f(x,y)+ \lim\limits_{(x,y) \to (2,5)}g(x,y)}\\=\frac{3}{3+7}=\frac{3}{10}.$$
