[1/(a+1)]-{(a+3)/[(a+1)(a-1)]}*{[(a-1)^2]/[(a+3)(a+4)}
=[1/(a+1)]-(a-1)/[(a+1)(a+4)]
=[(a+4)-(a-1)]/[(a+1)(a+4)]
5/[(a+1)(a+4)]