Calculating limits - general question

Hey!

I encountered a question in my homework that was: "Evaluate the limit, if it exists".

It is not possible to factor out the denominator of this equation. I tried dividing (x-2) into the equation and got a solution of x+1R8.

My question is: if I can't factor out the denominator of a rational equation, and the limit is asking where that equation would have the denominator at 0 (in the example 2) does this mean the limit does not exist?

I hope I made sense in my question.

Thanks!