1/(2+√5) + 1/(2-√5) = ((2-√5) +(2+√5)) / ((2-√5)*(2+√5) ) =
= ((2-√5 +2+√5)) / ((2-√5)*(2+√5) ) = 4/(4 - 5) = 4/-1 = - 4
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1/(2+√5) + 1/(2-√5) = ((2-√5) +(2+√5)) / ((2-√5)*(2+√5) ) =
= ((2-√5 +2+√5)) / ((2-√5)*(2+√5) ) = 4/(4 - 5) = 4/-1 = - 4