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

$$\frac{\sqrt{21}-5}2+\frac2{\sqrt{21}-5}=\frac{50-10\sqrt{21}}{2\sqrt{21}-10}=-5\frac{\sqrt{21}-5}{\sqrt{21}-5}$$


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


$$ \frac{2}{\sqrt{21}-5}=\frac{2}{\sqrt{21}-5}\frac{\sqrt{21}+5}{\sqrt{21}+5}=\cdots=-\frac{\sqrt{21}+5}{2} $$