(a²+3)/(a+1)(a-1)-(a+1)²/(a+1)(a-1)-1
=(a²+3-a²-2a-1)/(a+1)(a-1)-1
=(2-2a)/(a+1)(a-1)-1
=-2/(a+1)-1
=(-2-a-1)/(a+1)
=-(3+a)/(a+1)