How to establish a sum of squares inequality under constraint $xyz=1$?

Question

$$\frac{x^2}{(x-1)^2} + \frac{y^2}{(y-1)^2} + \frac{z^2}{(z-1)^2} \geq 1$$

with $xyz=1$

I have tried to define a Lagrange function, but do not know how to make it work.