Question: On simplification with radicals.

I need to move a term in the denominator, inside the radical sign in the numerator.  After some struggle, I can do it for a simple expression. But once the expression gets little more complicate, the method does not work.

Given expr:=sqrt(x*y)/x;  I want to force the "x" in the denominator inside the sqrt so I can simplify things. I can do this like this

restart;
expr1  := sqrt(x*y)/x;
expr1  := simplify(expr1,symbolic);
combine(expr1,symbolic);
algsubs(y/x=u,%);

But for the following similar expression, it does not work. Given expr:=sqrt(x^2+y^2)/x, I want to change to sqrt( (x^2+y^2)/x^2) or sqrt(1+ y^2/x^2) or sqrt(1 + u^2).  So the first step is as above, to force the x in denomiantor to go inside the radical. But the same steps do not work on this now

expr1:=sqrt(x^2+y^2)/x;
expr1:=simplify(expr1,symbolic);
combine(expr1,symbolic);

I tried radsimp(expr1); simplify(expr1,radical,symbolic); radnormal, I tried adding assuming positive everywhere. Nothing is working.

I am trying to convert an expression to be   (y/x) and then replace (y/x) to u.  BUt the first step is to get the x inside the radical and I am not sure how to do it for the second example and why it is failing. It is always hard for me in Maple to figure the right method to manipulate an expression.

Any suggestions?