We've been given the definition of a derivative as:
$f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$
We are asked to use this to find the derivative of the function $f(x)=\frac{1}{1-x}$ showing every step.
I can get to here: $f'(x)=\lim_{h\to0}\frac{1}{h-hx-h^2}-\frac{1}{h-hx}$
When I try using online equation solvers they just jump straight to the answer and I can't figure out how. Wolfram Alpha's step-by-step solution also doesn't give me any intermediate steps between this and the solution:
$\frac{1}{(x-1)^2}$
So, my question is, how do I solve a limit like the one above where every value in the denominator approaches 0?
(I'm guessing I'm just missing some algebraic tricks)