原式=[(a+1)²/(a+1)(a-1)-1/(a-1)]×(a-1)/a²
=[(a+1)/(a-1)-1/(a-1)]×(a-1)/a²
=(a+1-1)/(a-1)×(a-1)/a²
=a/(a-1)×(a-1)/a²
=1/a