x/(x-1)-1/lnx
=(xlnx-x+1)/(x-1)lnx
使用洛必达法则
=(lnx+1-1)/(lnx+(x-1)/x)
=xlnx/(xlnx+x-1)
上下求导
=(lnx+1)/(lnx+1+1)
=1/2