(2√2 + √12) / (5+2√6) = (2√2 + 2√3) / (5+2√6) = 2(√2 + √3) / (5+2√6) = 2(√2 + √3) (5-2√6) / (5+2√6) (5-2√6)
= 2(√2 + √3)(5-2√6) / (5^2 - (2√6)^2)
= 2(√2 + √3)(5-2√6) / (25 - 24)
= 2(√2 + √3)(5-2√6) / 1
= 2(5√2 - 2√12 + 5√3 - 6)
(2√2 + √12) / (5+2√6) = (2√2 + 2√3) / (5+2√6) = 2(√2 + √3) / (5+2√6) = 2(√2 + √3) (5-2√6) / (5+2√6) (5-2√6)
= 2(√2 + √3)(5-2√6) / (5^2 - (2√6)^2)
= 2(√2 + √3)(5-2√6) / (25 - 24)
= 2(√2 + √3)(5-2√6) / 1
= 2(5√2 - 2√12 + 5√3 - 6)