Prove that it is possible to isolate $z$ as a function of $(x,y)$ in $x^2 z^2-z^3 y x=0$ near the point $(1,1,1)$

Question

Prove that it is possible to isolate $z$ as a function of $(x,y)$ in $x^2 z^2-z^3 y x=0$ near the point $(1,1,1)$, but not near the origin.

I just need the idea for start, cause its supposed to be a maximum/minimum problem but i am totally lost, any hint will be well received.

Thanks