Prove a function $f(x)$ has a limit as $x$ approaches $1$. I am trying to prove the function $f(x) = (1-x)/(1-\sqrt{x})$ has a limit as $x$ approaches 1 using an epsilon definition. 
I've gotten as far as finding the limit is $2$ by factoring the numerator, as well as setting up the proof, which is as follows:
Let $\epsilon>0$ be given. Then there exists $\delta>0$ such that $|(1-x)/(1-\sqrt{x}) - 2| < \epsilon$ if $0 < x-1 < \delta$, $x$ element of the domain, and $1$ is an accumulation point.
Now, simplifying the absolute value gives $\left|\frac{(1-x) - 2(1-\sqrt{x})}{1-\sqrt{x}}\right| < \epsilon$, but now I do not know how to proceed.

hint:$\left|\dfrac{1-x}{1-\sqrt{x}}-2\right| = \left|\dfrac{-1+2\sqrt{x}-x}{1-\sqrt{x}}\right|=\dfrac{(1-\sqrt{x})^2}{|1-\sqrt{x}|}=|1-\sqrt{x}|= \dfrac{|1-x|}{1+\sqrt{x}}\leq |1-x|$, and the $\epsilon-\delta$ argument can be used.
