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2/√5-√3 - 1/√5+√3 =
2/(√5-√3)*(√5+√3)/√(5+√3) - 1/(√5+√3) * (√5-√3)/(√5-√3) =
(√5+√3)/(5-3) - (√5-√3)/(5 - 3) =
(√5+√3)/2 - (√5-√3)/2 =
[√5+√3 - (√5-√3)]/2 =
[[√5 + √3 - √5 + √3]/2 =
2√3/2 =
√3