Question

lim x->1 (x/x-1 - 1/ln(x))

Answer 1

use l'hospital's rule where appropriate

Answer 2

lhospitals rule u just take derivative of top and bottom separately

Answer 3

lim (x -> 1) [x/(x - 1) - 1/lnx]
lim (x -> 1) [(xlnx - (x-1)] / [(x-1)lnx]

Using L'Hospital's rule,
limit
lim (x -> 1) (1 + lnx - 1) / [lnx + (x-1)/x]
lim (x -> 1) (1/x) / (1/x + 1/x^2)
lim (x -> 1) 1 / (1 + 1/x)
1/2.