(a^3-4a^2b-a+4ab^2)/a(a-2b+1)
=(a^2-4ab+4b^2-1)/(a-2b+1)
=[(a-2b)^2-1]/(a-2b+1)
=(a-2b+1)(a-2b-1)/(a-2b+1)
=(a-2b-1)