KöMaL 2006 C871

Prove that if the expression $\frac{x^2}{(x-y)(x-z)} +\frac{y^2}{(y-x)(y-z)} +\frac{z^2}{(z-x)(z-y)}$ is well defined, then its value is independent of the values of the variables $x$, $y$and $z$.