Find all functions $f : N \to N$ such that $$\frac{f(x+y)+f(x)}{2x+f(y)}= \frac{2y+f(x)}{f(x+y)+f(y)}$$, for all $x, y$ in $N$.
Source: Indian Postal Coaching 2009 set 6 p6
Tags: functional equation, functional, algebra
Find all functions $f : N \to N$ such that $$\frac{f(x+y)+f(x)}{2x+f(y)}= \frac{2y+f(x)}{f(x+y)+f(y)}$$, for all $x, y$ in $N$.