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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?

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?

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Jonathan F. | Mathematics/writing tutor, with degrees in math and educationMathematics/writing tutor, with degrees ...

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?

Shawn L. | Master math tutor: excellent problem solverMaster math tutor: excellent problem sol...
5.0 5.0 (8 lesson ratings) (8)


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.