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