On Tue, 11 Sep 2007 12:12:49 -0500, <firstname.lastname@example.org> wrote in <news:email@example.com> in alt.math.undergrad:
> ooo <firstname.lastname@example.org> wrote:
>>If this is the limit,
>> lim[x -> 0] (x^4 - 1) / (x^3 - 1)
>>why do you want to factor it?
> Its the function of x
> Need limit value as it approaches zero
What ooo is getting at is that in this problem there's no need to factor the numerator or the denominator: the limit as x approaches 0 can be obtained directly from the fraction (x^4 - 1)/(x^3 - 1) without any manipulation.
If you were taking the limit as x approaches 1, it would be another story: then the numerator and denominator would both be approaching 0, and you *would* have to find a common factor of x^4 - 1 and x^3 - 1 to cancel. (As Arturo has already pointed out, x - 1 is such a factor.)