DE-BUNDESWETTBEWERB 2016 Problem 7

Find all functions $f$ that is defined on all reals but $\tfrac13$ and $- \tfrac13$ and satisfies $$f \left(\frac{x+1}{1-3x} \right) + f(x) = x$$ for all $x \in \mathbb{R} \setminus \{ \pm \tfrac13 \}$ .