Trouble with Uniform continuity calculation

So i have to prove that $\displaystyle f(x)=\frac{1}{\sqrt{x}}$ is uniformly continuous using the definition of uniform continuity...

aka I have to start with $\displaystyle |\frac{\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{c}}}{x-c} + \frac{1}{2\sqrt{c^3}}|$

and knowing that $\displaystyle |x-c|<\delta$, I have to make the first inequality less than $\displaystyle \epsilon$.

I am getting so lost in the calculation and this problem is due tomorrow, someone please help....