Limx>1x^2-x+1/(x-1)^2极限,

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Limx>1x^2-x+1/(x-1)^2极限,Limx>1x^2-x+1/(x-1)^2极限,Limx>1x^2-x+1/(x-1)^2极限,因为Limx>1(x-1)^2/(x^2-x+1)=0/

Limx>1x^2-x+1/(x-1)^2极限,
Limx>1x^2-x+1/(x-1)^2极限,

Limx>1x^2-x+1/(x-1)^2极限,
因为Limx>1 (x-1)^2/(x^2-x+1)
=0/(1-1+1)
=0
所以
原式=∞

x->1时,分子不为0,分母为0,则结果为∞