I've been banging my head all day long over this question, would apprecate some help :)
$f(x) = \frac{1}{x^2-1} - \frac{a}{x^3-1},\qquad a\in\mathbb{R}.$ For which values of $a$ does $\lim\limits_{x \to 1} f( x)$ exist?
Also it was requested to use only the $\epsilon$-$\delta$ definition.