lim（3/（x^3-1)-1/(x-1),x趋于1,求极限

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lim（3/（x^3-1)-1/(x-1),x趋于1,求极限
lim（3/（x^3-1)-1/(x-1),x趋于1,求极限

lim（3/（x^3-1)-1/(x-1),x趋于1,求极限
lim [3/(x-1)(x²+x+1) -(x²+x+1)/(x-1)(x²+x+1)] x趋于1
=lim(3-x²-x-1)/(x-1)(x²+x+1) x趋于1
=lim -(x+2)(x-1)/(x²+x+1) x趋于1
=lim-(x+2)/(x²+x+1) x趋于1 用x=1代入
=-1

原式=lim[3/(x-1)(x²+x+1)-1/(x-1)]
=lim-(x-1)(x-2)/(x-1)(x²+x+1)
=lim(2-x)/(x²+x+1)
=1/3

解 limx→1{3/（x^3-1）-1/（x-1）}
=limx→1{3/[(x-1)(x²+x+1)]-1/（x-1）}通分得
=limx→1{（-x^2-x+2）/[（x-1）(x²+x+1)]}
=limx→1{-（x+2）/（x²+x+1）}
=-3/3
=-1

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