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】：limx→0[1/x-1/(e^x-1)] =limx→0{(e^x-1-x)/[x(e^x-1)]} =limx→0[(e^x-1-x)/x²] =limx→0[(e^x-1)/2x-1/2]}