[tex]\dfrac{2\sqrt3-\sqrt6}{3\sqrt6+2\sqrt3}=\\
\dfrac{(2\sqrt3-\sqrt6)(3\sqrt6-2\sqrt3)}{(3\sqrt6+2\sqrt3)(3\sqrt6-2\sqrt3)}=\\
\dfrac{6\sqrt{18}-12-18+2\sqrt{18}}{54-12}=\\
\dfrac{-30+8\sqrt{18}}{42}=\\
\dfrac{-30+24\sqrt{2}}{42}=\\
\dfrac{-5+4\sqrt{2}}{7}
[/tex]
