[a/(a-1)-a^2/(a^2-1)]÷[1-1/(a+1)]
=[a(a+1)-a^2]/[(a-1)(a+1)]÷[(a+1-1)/(a+1)]
=a/[(a-1)(a+1)]÷[a/(a+1)]
=a/[(a-1)(a+1)]*(a+1)/a
=1/(a-1)