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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.

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    **Hint:** Note that $x^3 - 1 = (x-1)(x^2 + x + 1)$, and then subtract the two fractions by finding the least common denominator.2012-01-13

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