Use the definition of the derivative to find f'(x)

f(x) = 1/(x-1)

I tried doing it, but have no idea how to do it.. I also tried the derivative "shortcut" and still got the wrong answer..

The answer is -1/[(x-1)^2]

I tried using the shortcut and I ended up getting 0.. But how do they get -1/(x-1)^2??