答:
两种方法都可以,楼主可能计算错误了
用洛必达法则是可以的,因为分母为0,分子为0,符合洛必达法则
用因式分解也可以:
(x^3-3x+2) / (x^3-x^2-x+1)
=(x^3-x-2x+2) /(x^3-x^2-x+1)
=[ (x-1)(x+1)x-2(x-1) ] / [(x-1)x^2-(x-1)]
=(x-1) (x^2+x-2) / [(x-1)(x^2-1)]
=(x-1)(x-1)(x+2) / [ (x-1)(x-1)(x+1)]
=(x+2)/(x+1)
=3/2