Why does √x · (1/x) = 1/√x?

[Altami]

How is squareroot(x)*(1/x)= 1/square root x

can somebody please explain this? I think I am having a brain lockup...

 

[mathman]

Let y=√x, the x=y². So √x/x = y/y² = 1/y = 1/√x.

 

[Altami]

Let y=√x, the x=y². So √x/x = y/y² = 1/y = 1/√x.

Thank you! For some reason I couldn't think of the reason to make the statement true.

Life saver!