化简：（a的平方-1）分之a的平方+3）-（a-1)分之（a+1)+1=

原式=(a²+3)/(a+1)(a-1)-(a+1)²/(a+1)(a-1)+(a+1)(a-1)/(a+1)(a-1)
=[(a²+3)-(a²+2a+1)+(a²-1)]/(a+1)(a-1)
=(a²-2a+1)/(a+1)(a-1)
=(a-1)²/(a+1)(a-1)
=(a-1)/(a+1)