How do I simplify $\frac{\sqrt{21}-5}{2} + \frac{2}{\sqrt{21} - 5}$? 
How do I simplify the following equation?
$$\frac{\sqrt{21}-5}{2} + \frac{2}{\sqrt{21} - 5}$$

I have no idea where to start. If I multiply either fraction by its denominator I will still end up with a square root. I know the end result should be $-5$.

$$\frac{\sqrt{21}-5}{2}+\frac{2}{\sqrt{21}-5}=\frac{\sqrt{21}-5}{2}+\frac{2(\sqrt{21}+5)}{(\sqrt{21}-5)(\sqrt{21}+5)}=\frac{\sqrt{21}-5}{2}+\frac{2\sqrt{21}+10}{-4}=\frac{2\sqrt{21}-10}{4}-\frac{2\sqrt{21}+10}{4}=\frac{2\sqrt{21}-10-2\sqrt{21}-10}{4}=-5$$
