## last independence and RV question

Here I want to show that given Y=Z/X is indep. of Z and X, where X,Z>0 show that Y is a constant.

The hints I got are to consider:
$Cov(Y,X)$
$Cov(Y^2,X^2)$
both of which equal 0 since
$Cov(Y^r,X^s)=E(Y^rX^s)-E(Y^r)E(X^s)=0$
then defining a new variable U=1/Y which is supposed to help somehow
and then considering V(Y).

I need help in understanding how to tie these hints together to get the final answer (V(Y)=0)