Rationalize

$1\over1+{1\over\sqrt{3}}+2$

Multiply top and bottom by root3 and combine 1 + 2.

$\sqrt{3}\over3\sqrt{3}+1$

Multiply top and bottom by $3\sqrt{3}-1$

$\sqrt{3}(3\sqrt{3}-1)\over(3\sqrt{3}+1)(3\sqrt{3}-1)$

$9 - \sqrt{3}\over26$