Rationalize the denominator of $\frac{2}{3\sqrt{5} + \sqrt{11}}$ and write your answer in the form $\displaystyle \frac{A\sqrt{B} + C\sqrt{D}}{E}$, where $B < D$, the fraction is in lowest terms and all radicals are in simplest radical form. What is A + B + C + D + E?

Guest Jan 18, 2022