express3square root5-square root3/2square root5+3square root3
recall that (a+b)(a-b) = a^2-b^2
then multiply top and bottom by 2√5-3√3 and you have
(3√5-√3)(2√5-3√3)
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(2√5+3√3)(2√5-3√3)
6*5 - 2√15 - 9√15 + 3*3
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20-27
= (11√15 - 39)/7