Here's a limit where Maple stalls:

Ø     limit((sqrt(h^2+4*h+5)-sqrt(5))/h,x=0,right);
Ø      

The best it can do is

(  sqrt(h^2 + 4*h + 5) - sqrt(5) ) /h

but after a little algebraic manipulation the answer is 2/sqrt(5)

Can Maple's performance be improved?

Alla