[tex]\frac{2}{\sqrt5+\sqrt3}+\frac{1}{\sqrt3+\sqrt2}+\frac{4}{\sqrt9+\sqrt5}=\\
\frac{2(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}+\frac{\sqrt3-\sqrt2}{(\sqrt3+\sqrt2)(\sqrt3-\sqrt2)}+\frac{4(\sqrt9-5)}{(\sqrt9-\sqrt5)(\sqrt9+\sqrt5)}=\\
\frac{2(\sqrt5-\sqrt3)}{2}+\sqrt3-\sqrt2+\frac{4(\sqrt9-\sqrt5)}{4}=\\
\sqrt5-\sqrt3+\sqrt3-\sqrt2+3-\sqrt5=3-\sqrt2[/tex]
