令a=2000
则原式=[a³-2a-(a-2)]/[a³+a²-(a+1)]
=[a²(a-2)-(a-2)]/[a²(a+1)-(a+1)]
=(a-2)(a²-1)/[(a+1)(a²-1)]
=(a-2)/(a+1)
=1998/2001
=666/667