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)/x^2 =lim(x→0)(e^x-1)/(2x) =lim(x→0)x/(2x) =1/2