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= √15+√3 / √15 - √3 x √15+√3 / √15+√3
= (√15+√3)(√15-√3) / (√15)²-(√3)²
= 15+2√45-3 / 15-3
= 12+2√9√5 / 12
= 12/12 + 6√5/12
= 1 + ½√5