/sci/ - Science & Math

how do i go about solving this without using l'hopital

I've tried using maclaurin series to approximate the values of the tricky functions at 0 but I end up with all the values on the top cancelling

From their maclaurin series i think both the exponential and log functions should be approximated by x^2, but then they are cancelled out by the -2x^2, so i end up with 0/x^6, and wolfram tells me the limit should be 9/11.

i must be doing something wrong but i cant pinpoint it

send help