∵a是一元二次方程x²-2x-2=0的正实数根
∴a²-2a-2=0
∴(a-1)²=3,∴a=1+√3
∴(a²-1)/(a²+a)÷[a- (2a-1)/a]
=[(a+1)(a-1)/a(a+1)]÷[(a²-2a+1)/a]
=[(a-1)/a]÷[(a-1)²/a]
=[(a-1)/a]×[a/(a-1)²]
=1/(a-1)
=1/(1+√3-1)
=√3/3