Specific inequality Let $x,y,z$ be different real numbers . Prove that:
$$\frac{x^2y^2+1}{(x-y)^2}+\frac{y^2z^2+1}{(y-z)^2}+\frac{z^2x^2+1}{(x-z)^2} \geq \frac{3}{2}$$

Hint :
We have Dao Hai Long inequality :
$$\sum \frac{a+b}{a-b}.\frac{b+c}{b-c}=-1$$
So :
$$\sum \frac{(a+b)^2}{(a-b)^2} \geq 2$$
So:
$$\sum \frac{ab}{(a-b)^2} \geq \frac{-1}{4}  (1)$$
Then :
$$\sum \frac{1-ab}{a-b}=-1$$
So:
$$\sum \frac{(1-ab)^2}{(a-b)^2} \geq 2 (2)$$
From (1) and (2) we have solution
