Originally Posted by ColinsMum
So it is true that sqrt(x)/sqrt(y) = sqrt(x/y) WHEN BOTH SIDES ARE DEFINED, but it isn't true without that condition.

Both sides are defined if and only if x>=0 and y>0.

The RHS is defined and the LHS is undefined if and only if x<=0 and y<0

It never happens that the RHS is undefined and the LHS is defined.

Both sides are undefined if and only y=0 or (x<0 and y>0) or (x>0 and y<0).