Minimum value of rational expression 
If $x,y,z$ are distinct real number, Then minimum value of   $\displaystyle \left(\frac{x}{y-z}\right)^2+\left(\frac{y}{z-x}\right)^2+\left(\frac{z}{x-y}\right)^2$

Try: $$\left(\frac{x}{y-z}\right)^2+\left(\frac{y}{z-x}\right)^2+\left(\frac{z}{x-y}\right)^2\geq \frac{x^2+y^2+z^2}{(x-y)^2+(y-z)^2+(z-x)^2}$$
could some help me to solve this, thanks

we have to prove that $$ \left(\frac{x}{y-z}\right)^2+\left(\frac{y}{z-x}\right)^2+\left(\frac{z}{x-y}\right)^2\geq 2$$
this is true since this inequality is equivalent to $${\frac { \left( {x}^{3}-y{x}^{2}-z{x}^{2}-{y}^{2}x+3\,zyx-{z}^{2}x+{y}
^{3}-z{y}^{2}-{z}^{2}y+{z}^{3} \right) ^{2}}{ \left( y-z \right) ^{2}
 \left( -z+x \right) ^{2} \left( x-y \right) ^{2}}}
\geq 0$$
