What are the possible x values for finding a limit in this problem?

[beartopper]

This is very basic. I have asked some friends and they don't know. I have tried resolving it by long division, and can see where the 1 comes from but the remainder is 1. I have gone back to the basics, but the operands are multicative. ie 1/a * a = 1
What is the algebra of this

The problem in taking limits: Notice that, by division x-2/x-3 = 1 + 1/ x-3.

 

[gb7nash]

What is x approaching on your limit?

 

[symbolipoint]

This is not what you meant:

x-2/x-3 = 1 + 1/ x-3

You wished to say, \frac{x-2}{x-3}=1+\frac{1}{x-3}

What does x approach for which you want to find a limit? Is the expression defined at that x value?

Most likely you are interested in one of these:

• 
  x approaches negative infinity
  x approaches 0
  x approaches infinity
  x approaches +3