Proving that $f(x) = (x + 1) / (x^2 - 1)$ does not have a limit at $1$

Question

I am trying to prove that the function $f:(-1,1) \to \mathbb{R}$ defined by $f(x) = (x+1)/(x^2-1)$ does not have a limit at $1$ through an epsilon-delta proof. So far, I have attempted to prove this by assuming the function has a limit, L, at 1. I just can't seem to arrive at a contradiction. Any suggestions? Thanks.

Answer 1

HINT:

Note that $\lim_{x\to 1^-}\frac{1}{x-1}=-\infty$ since for any $B<0$, $\frac{1}{x-1}<B$ whenever $1+\frac1B <x<1$.

Now, apply analogous logic to the right-sided limit and show that the limits are not equal.