Limit of $\frac{x^5-1}{x^2-1}$ I need to determine if the following limit exists.
$$\lim_{x\to 1}\frac{x^5-1}{x^2-1}$$
I've already proved using L'Hospital that this limit exists and should equal to $\frac{5}{2}$, but unfortunately I'm not allowed to used anything more than basic analysis for functions, i.e. basic definitions of convergence(at most continuity).

using Horner's method:
$$x^5 -1 =(x-1)(x^4 +x^3 +x^2 +x+1)$$
$$x^2 -1=(x-1)(x+1)$$
