# How to calculate <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeX

How to calculate $\underset{x\to 1}{lim}\frac{\left({x}^{2}-3x+2\right)}{\left(x-1\right)\left({x}^{3}-1\right)}$
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Isla Klein
Notice that by writing
$f\left(x\right)=\frac{x-2}{{x}^{2}+x+1}$
you have that
$\frac{x-2}{{x}^{3}-1}=\frac{x-2}{{x}^{2}+x+1}\cdot \frac{1}{x-1}=\frac{f\left(x\right)}{x-1}$
Notice, moreover, that as $x\to 1$, $f\left(x\right)\to -1/3$. Meanwhile, depending on which direction you approach from, $1/\left(x-1\right)\to ±\mathrm{\infty }$. The end result is clear: your one-sided limits go to $+\mathrm{\infty }$ and $-\mathrm{\infty }$ and hence the limit overall does not exist.