lim (x→1) (x/(x-1)-1/(lnx))
=lim (x→1) [xlnx-(x-1)]/[(x-1)(lnx)] (0/0)
=lim (x→1) (lnx+1-1)]/[lnx+1-1/x]
=lim (x→1) xlnx/(xlnx+x-1) (0/0)
=lim (x→1) (lnx+1)/(lnx+1+1)
=1/2