How to prove this algebra question? If $x=y^2+z^2$,  $y=x^2+z^2,$ and $z=x^2+y^2$ then show that $$\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+1}=1$$

hint
$x-y=y^2-x^2=(y-x)(y+x)$. So either $x=y$ or $x+y+1=0$. Do the same with other pairs.
