Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 73

$\dfrac{-7}{12+6\sqrt{11}}$

Multiplying by the conjugate of the numerator, then the rationalized-numerator form of the given expression, $ \dfrac{2-\sqrt{11}}{6} ,$ is \begin{array}{l}\require{cancel} \dfrac{2-\sqrt{11}}{6}\cdot\dfrac{2+\sqrt{11}}{2+\sqrt{11}} \\\\= \dfrac{(2)^2-(\sqrt{11})^2}{6(2)+6\sqrt{11}} \\\\= \dfrac{4-11}{12+6\sqrt{11}} \\\\= \dfrac{-7}{12+6\sqrt{11}} .\end{array}