Limits question 2 parts?

Question

part I
limx--> 9

1/(x – 9) – 18/(x^2 – 81)

1________ 18
----------- – --------------------
x – 9 x * x – 81


(x – 9)(x + 9)

1_________ 18
----------- – --------------------
x – 9 (x – 9)(x + 9)

this is as far as i got, but i know the answer isn't 0, or undefined.

Part II

lim --> 9

1/x – 1/9
-----------
x-9

note: if someone has some kind of methodology with limits, that would help a lot more, i.e., break it down. thanx!

Answer 1

♠ thus 1/(x – 9) – 18/(x^2 – 81) =
= (x+9 –18) / ((x-9) *(x+9)) = 1/(x+9) =1/18;
♣ thus (1/x –1/9)/ (x-9) = (9-x) /(9x*(x-9)) =
= -(x-9) /(9x*(x-9)) =-1/(9x)= -1/81;
nothing in particular, just experience;