lim[x->2] (x^2 - x + 6)/(x - 2)

I'm not sure the best way to solve this... but here's what I did:

after doing polynomial division, I got:

lim[x->2] (x+1+ 8/(x-2))

So, by reasoning, I see that the limit as x approaches 2 from the left does not equal the limit as x approaches 2 from the right (negative and positive infinity). Therefore, this limit does not exist.

My solutions manual says that the limit "does not exist since x - 2 -> 0 but x^2 - x + 6 -> 8 as x -> 2."

Someone please tell me what my book's explanation means.