Given the function: f(x) = (x2-x-2)/(x2-2x-3) Biggest possible domain of cource

Question

Given the function:
f(x) = (x2-x-2)/(x2-2x-3)
Biggest possible domain of cource x not equal -1 or 3. Then continuous for all x exept -1 and 3.. right? :) Then the real question: how to extend the function so that is will be continuous on as big set as possible? Please help!! Thanks!
Given the function:
f(x) = (x2-x-2)/(x2-2x-3)
Biggest possible domain of cource x not equal -1 or 3. Then continuous for all x exept -1 and 3.. right? :) Then the real question: how to extend the function so that is will be continuous on as big set as possible? Please help!! Thanks!

Explanation / Answer

you have to brake down the equations:
You have x^2-x-2 on the top so first work with that equation to back it down if that is posible.    You would get (x+1)(x-2).   Next you have to work with the bottom and do the same. You start with x^2-2x-3.    You would get (x+1)(x-3). Then you want to reduse the whole equation so that you'll have: (x-2)/(x-3) You will have one answer that doesn't give anything out, and you also have one that will give you an answer of zero if that is something that you wont to have.

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