Prove that function is odd, without the explicit function

Question

So I have the following $f: \mathbb{R} \rightarrow \mathbb{R}$. Prove that $f$ is odd given the following relation:

$$3f(x) + 2f(-x)=\frac{x}{x^2+1}$$

Answer 1

Hint: change $x$ to $-x$, and add the two equations.