Answer
$-\frac{3}{\sqrt 2+\sqrt {11}}$
Work Step by Step
$\frac{\sqrt 2-\sqrt {11}}{3}=\frac{\sqrt 2-\sqrt {11}}{3}\frac{\sqrt 2+\sqrt {11}}{\sqrt 2+\sqrt {11}}=\frac{\sqrt 2(\sqrt 2)+\sqrt 2(\sqrt {11})-\sqrt {11}(\sqrt 2)-\sqrt {11}(\sqrt {11})}{3(\sqrt 2+\sqrt {11})}=\frac{(\sqrt 2)^2-(\sqrt {11})^2}{3(\sqrt 2+\sqrt {11})}=\frac{2-11}{3(\sqrt 2+\sqrt {11})}=\frac{-3(3)}{3(\sqrt 2+\sqrt {11})}=\frac{-3}{\sqrt 2+\sqrt {11}}=-\frac{3}{\sqrt 2+\sqrt {11}}$
