If i have rational function and it has a numerator that can be factored and the denominator is already factored out would I simplify by factoring the numerator?

Question

The question is:

((x^2)-4)/ ((x-2)(x+3))

and then cancelling out the x-2 from both the denominator and the numerator leaving me with (x+2)/(X+3)? And then go from there to find the limit?

Answer 1

Yes, you can simplify it that way, but then you need to note that your new Domain is all real numbers with the exception of 2.

Domain = R - {2} is how you would notate it.

 

Do you understand why? Do you know what makes two equations equilvent?

Answer 2

Danielle,

To echo/amplify Jon's point: you can of course cancel (x-2), but keep in mind there is a conditon for you to be able to do that: x-2 /= 0; or in other words, the cancellation is only valid for x /= 2.