求极限limx→0[1/x-1/(ex-1)]．

求极限lim_x→0[1/x-1/(e^x-1)]．
【正确答案】：lim_x→0[1/x-1/(e^x-1)] =lim_x→0{(e^x-1-x)/[x(e^x-1)]} =lim_x→0[(e^x-1-x)/x²] =lim_x→0[(e^x-1)/2x-1/2]