\[\begin{array}{l} {\text{Пусть }}x,y,z \in \mathbb{R}\backslash \left\{ 1 \right\},{\text{ }}xyz = 1. \hfill \\ {\text{Докажите неравенство:}} \hfill \\ \frac{{{x^2}}}{{{{\left( {x - 1} \right)}^2}}} + \frac{{{y^2}}}{{{{\left( {y - 1} \right)}^2}}} + \frac{{{z^2}}}{{{{\left( {z - 1} \right)}^2}}} \geqslant 1. \hfill \\ \end{array}\]