[tex]\displaystyle\\
\frac{ \sqrt{5} }{2-\sqrt{5} }+ \frac{2}{2+\sqrt{5} } =\\\\\\
= \frac{ \sqrt{5} (2+\sqrt{5})}{(2-\sqrt{5})(2+\sqrt{5}) }+ \frac{2(2-\sqrt{5})}{(2-\sqrt{5})(2+\sqrt{5})}=\\\\\\
= \frac{ 2\sqrt{5} +5}{4-5 }+ \frac{4-2\sqrt{5}}{4-5}=\frac{ 2\sqrt{5} +5+4-2\sqrt{5}}{-1}= \frac{5+4}{-1} =\boxed{-9}
[/tex]
