lim【1/x-1/(e^x-1)】
=lim (e^x-1-x)/x(e^x-1)
=lim (e^x-1)/[(e^x-1)+xe^x]
=lim 1/[1+xe^x/(e^x-1)]
=lim 1/{1+e^x/[(e^x-1)/x]}
=1/(1+1/1)
=1/2