lim x趋向于1 [1/(x^2-3x+2)-2/(x^2-4x+3)]=
题目
lim x趋向于1 [1/(x^2-3x+2)-2/(x^2-4x+3)]=
答案
x²-3x+2=(x-2)(x-1)
x²-4x+3=(x-3)(x-1)
1/(x²-3x+2)-2/(x²-4x+3)
=1/[(x-2)(x-1)]-2/[(x-3)(x-1)]
=[(x-3)-2(x-2)]/[(x-3)(x-2)(x-1)]
=(1-x)/[(x-3)(x-2)(x-1)]
=-1/[(x-3)(x-2)]
lim [1/(x²-3x+2)-2/(x²-4x+3)]
=lim -1/[(x-3)(x-2)]
=-1/[(1-3)(1-2)]
=-1/2
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