Simplify multivariable expression

Question

Problem is to simplify this expression. I have no idea how to factor either part of the fraction.

$$ \frac { x^4(y-z)+ y^4 (z-x)+ z^4(x-y)}{(x+y)^2 + (y+z)^2 + (x+z)^2} $$

Answer 1

Hint: Note that the numerator vanishes when $x=y$ or $x=z$ or $y=z$. So try to divide the numerator by $(x - y) (x - z) (y - z) $.