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\frac{2}{\sqrt3}=\frac{2*\sqrt3}{\sqrt3*\sqrt3}=\frac{2\sqrt3}{3}
\frac{3}{\sqrt5-2}=\frac{3(\sqrt5+2)}{(\sqrt5-2)(\sqrt5+2)}=\frac{3\sqrt5+6}{5-2}=\frac{3(\sqrt5+2)}{3}=\sqrt5+2
\frac{2}{3+\sqrt5}=\frac{2(3-\sqrt5)}{(3+\sqrt5)(3-\sqrt5)}=\frac{6-2\sqrt5}{9-5}=\frac{2(3-\sqrt5)}{4}=\frac{3-\sqrt5}{2}