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Rationalize the denominator of $\frac{2}{3\sqrt{5} + 2\sqrt{11}}$ 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 $A+B+C+D+E$?

 Jan 18, 2021
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Multiply top and bottom of the given  by   3 sqrt5 - 2sqrt11   to get

 

 

2 (3sqrt5 - 2 sqrt11 ) / (45-44)

= (6 sqrt5 - 4 sqrt11)/1                     ....take it from here...

 Jan 19, 2021

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