原式=[(a-1)/a -(a-2)/(a+1)]÷ a(2a-1)/(a+1)²
=[(a-1)(a+1)-a(a-2)]/a(a+1)× (a+1)²/a(2a-1)
=(2a-1)/a(a+1)×(a+1)²/a(2a-1)
=(a+1)/a²
∵a²-a-1=0
∴a²= a+1
∴原式=(a+1)/(a+1) =1
原式=[(a-1)/a -(a-2)/(a+1)]÷ a(2a-1)/(a+1)²
=[(a-1)(a+1)-a(a-2)]/a(a+1)× (a+1)²/a(2a-1)
=(2a-1)/a(a+1)×(a+1)²/a(2a-1)
=(a+1)/a²
∵a²-a-1=0
∴a²= a+1
∴原式=(a+1)/(a+1) =1