express3square root5-square root3/2square root5+3square root3

Answer 1

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)
--------------------
(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