`#tnvt`
`\frac{6}{\sqrt{2}-\sqrt{3}+3}`
`=\frac{6}{(\sqrt{2}-\sqrt{3})+3}`
`=\frac{6(\sqrt{2}-\sqrt{3}-3)}{(\sqrt{2}-\sqrt{3})^2-3^2}`
`=\frac{6\sqrt{2}-6\sqrt{3}-18}{2-2\sqrt{6}+3-9}`
`=\frac{-2(-3\sqrt{2}+3\sqrt{3}+9)}{-2(2+\sqrt{6})}`
`=\frac{(-3\sqrt{2}+3\sqrt{3}+9)(\sqrt{6}-2)}{6-4}`
`=\frac{-6\sqrt{3}+6\sqrt{2}+9\sqrt{2}-6\sqrt{3}+9\sqrt{6}-18}{2}`
`=\frac{15\sqrt{2}-12\sqrt{3}+9\sqrt{6}-18}{2}`
