<s>[INST] 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 $$\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+1}=1$$
 [/INST] $$x^2+y^2+z^2=x(x+1)\implies\dfrac x{x+1}=?$$
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