lim x趋向于1 [1/(x^2-3x+2)-2/(x^2-4x+3)]=
问题描述：
lim x趋向于1 [1/(x^2-3x+2)-2/(x^2-4x+3)]=
答
1/(x^2-3x+2)-2/(x^2-4x+3)
=1/(x-2)(x-1)-2/(x-3)(x-1)
=(x-3-2x+4)/(x-1)(x-2)(x-3)
=-1/(x-2)/(x-3)
所以极限=-1/(-1)*(-2)=-1/2
答
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