TITLE: limit involving rational function and square root
QUESTION [5 upvotes]: When working some exercise problems in my calc book, I came across this limit in which I do not know how to tackle.  It is
$$\lim_{x\to\infty}\frac{1-\frac{x}{x-1}}{1-\sqrt{\frac{x}{x-1}}}$$
I feel like there is a trick to this one, maybe use L'Hopital's rule or something.  I tried to multiplying by the conjugate but it turned ugly real fast.  Any tips will be helpful.

REPLY [3 votes]: Hint:
$$\frac{1-u}{1-\sqrt{u}}=1+\sqrt{u}$$