From the Indian National Mathematics Olympiad 1992:
Determine all functions $f: \mathbb R -[0,1] \rightarrow \mathbb R$, satisfying the functional relation:
$$f(x) + f \left( \frac{1}{1-x} \right) = 2\frac{1 - 2x}{x(1-x)}$$
where $x$ is a real number and not equal to $0$ or $1$
First plug in $$x=\frac{1}{1-x}$$ Then plug in $$x=\frac{x-1}{x}$$ You'll get a system of 3 equations which you can add and substract to get $f(x)$,since on the olympiad you have much time I'll leave the replacing of the x's part to you.