Question 991482
you are correct
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(5sqrt(5) - 3sqrt(3)) / (4sqrt(5) + 2sqrt(3))
multiply denominator and numerator by (4sqrt(5) - 2sqrt(3))
((5sqrt(5) - 3sqrt(3)) * (4sqrt(5) - 2sqrt(3))) / (16*5 - 4*3) =
(20*5 -22sqrt(15) +6*3) / 68 =
(118 - 22sqrt(15)) / 68 =
2(59 - 11sqrt(15)) /68 =
(59 - 11sqrt(15)) / 34