Please,

if we have:

lim(x to 1) ((x/(x-1)-1/lnx)

then we get:

lim(x to 1) ((xlnx-x+1)/(xlnx-lnx))

then we take x=1:

lim(x to1)((ln(1)+1-1) / (ln(1)-ln(1))

we get 0/0

and can apply LH:

but NOW:

How do we get NOW lim(x to1)((xlnx)/(xlnx+x-1)???

What is the inversion doing here?

Many thanks!