Answer
$\frac{-(x+1)}{x^{2}+x+1}$
Work Step by Step
We simplify:
$\displaystyle \frac{1-x^{2}}{x^{3}-1}=\frac{(1-x)(1+x)}{(x-1)(x^{2}+x+1)}=\frac{-(x-1)(1+x)}{(x-1)(x^{2}+x+1)}=\frac{-(x+1)}{x^{2}+x+1}$
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