原式=1/(a-1)+ (a-2)²/(a-1)×(a+1)× a+1/a-2
(到这一步,(a-2)²和a-2化简成a-2,(a-1)×(a+1)和 a+1化简成a-1)
=1/(a-1)+ a-2/a-1
(合并同类项)
=(1+ a-2)/a-1
=1
∴无论a为何值,原式值都为1
原式=1/(a-1)+ (a-2)²/(a-1)×(a+1)× a+1/a-2
(到这一步,(a-2)²和a-2化简成a-2,(a-1)×(a+1)和 a+1化简成a-1)
=1/(a-1)+ a-2/a-1
(合并同类项)
=(1+ a-2)/a-1
=1
∴无论a为何值,原式值都为1