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?
+128460 2 3sqrt 5 + sqrt 11
____________________ * ________________ =
3sqrt 5 - sqrt 11 3sqrt 5 + sqrt 11
2 ( 3sqrt 5 + sqrt 11)
____________________ =
(3sqrt 5)^2 - (sqrt 11) ^2
6 sqrt 5 + 2sqrt 11
___________________ =
45 - 11
6sqrt 5 + 2 sqrt 11
________________ =
34
3 sqrt 5 + 1 sqrt 11
_____________________
17
A + B + C + D + E =
3 + 5 + 1 + 11 + 34 = 54
