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