Let the following functional equation be given:
$$\frac{f(x+y)+f(2y)}{f((x+y)2y)}=\frac{f(x)+f(y)}{f(xy)}+y.$$
where function $f:(0,\infty)\rightarrow (0,\infty)$. I'm looking for any continuous solution of this equation, but I have a hard time to do this. Maybe such a solution doesn't exist? On the other hand, very similar equation
$$\frac{f(x+y)+f(2y)}{f((x+y)2y)}=\frac{f(x)+f(y)}{f(xy)}+2y$$
has infinitely many continuous solutions (i.e. $f(x)=\frac{a}{x}$, $a>0$).