After struggling with this limit for a while, I would really, really appreciate your help with solving this problem.

Let be positive real numbers.Withoutusing the l'Hôpital's rule, find the limit

I tried every method of attack known to me, but to no avail; substitution; trying to utilize the identity , ... nothing seemed to work.

Mathematica says the limit should be , but I have no idea how to arrive at that.

I'd be very grateful for any help.