MathNet 2008-part-04 — 165 problems (EN–VI) Question 112

(Lishunov Vitalii) $\frac{1}{x-y} + \frac{1}{y-z} + \frac{1}{z-x} = \frac{3}{2}$ is true for some real numbers $x$, $y$, $z$. What value may expression $\frac{1}{(x-y)^2} + \frac{1}{(y-z)^2} + \frac{1}{(z-x)^2}$ have?