lim（X－＞1）（X／lnX－1／（X一1））＝?

lim（X－＞1）[X／lnX－1／（X一1）]
=lim（X－＞1）[x(x-1)-lnx] / [(x-1)lnx] 0/0形,用洛必达
=lim(x->1) [2x-1-1/x] / [lnx-(x-1)/x]
=lim(x->1) [2x^2-x-1] / [xlnx-x+1] 0/0形,用洛必达
=lim(x->1) (4x-1) / [lnx-x*1/x-1]
=lim(x->1) (4x-1) / (lnx-2)
=(4-1)/(0-2)
=-3/2