your answer is not correct
put x^-1=u
->
x^-2=u^2
x^-3=u^3
now: when x=1 --->u=1
so , we have
nominator=3u^3+2u^2-5
denominator=u-1*u+2=u^2+u-2
by long dividing
=
3u
+
nominator=-u^2+6u-5
+
denominator=u^2+u-2
now
nominator/denominator-
u^2-6u+5/u^2+u-2
=u-1*u-5/u-1*u+2=u-5/u+2
--->
lim 3u-lim u-5/u+2 when u=1
=minus4/3-3
=3+3/4
=3/13
