用两次洛必达法则
通分
lim(x/(x-1) -1/lnx)= lim(xlnx -x +1)/(x-1)lnx =lim(1+lnx-1)/((x-1)/x+lnx) (一次洛必达)
=lim(xlnx)/(x-1+xlnx) = lim(1+lnx)/(1+1+lnx) (二次洛必达)
=lim(1+lnx)/(2+lnx) (x->1,lnx=0)
=1/2