\frac{1}{a}+\frac{1}{b}=
=\frac{1}{\sqrt3-\sqrt2}+\frac{1}{\sqrt3+\sqrt2}=
=\frac{\sqrt3+\sqrt2}{\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}+\frac{\sqrt3-\sqrt2}{(\sqrt3+\sqrt2)(\sqrt3-\sqrt2)}=
=\frac{\sqrt3+\sqrt2}{3-2}+\frac{\sqrt3-\sqrt2}{3-2}=
=\sqrt3+\sqrt2+\sqrt2-\sqrt2=2\sqrt3