Simple almost linear functional equation

Question

I'd like to solve functional equation: $f(x+y)=\frac{f(x)+f(y)}{1-f(x)f(y)}.$

I've managed to get: $f(0)=0,f(n)=0$ for all $n\in N$; $f(\frac{1}{2})=0$; $f(-x)=-f(x)$. I'll be grateful for any help.