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How do you 1/(x^3+1) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
  1   
------
 3    
x  + 1
$$\frac{1}{x^{3} + 1}$$
1/(x^3 + 1)
Fraction decomposition [src]
1/(3*(1 + x)) - (-2 + x)/(3*(1 + x^2 - x))
$$- \frac{x - 2}{3 \left(x^{2} - x + 1\right)} + \frac{1}{3 \left(x + 1\right)}$$
    1           -2 + x    
--------- - --------------
3*(1 + x)     /     2    \
            3*\1 + x  - x/
Numerical answer [src]
1/(1.0 + x^3)
1/(1.0 + x^3)
Combinatorics [src]
         1          
--------------------
        /     2    \
(1 + x)*\1 + x  - x/
$$\frac{1}{\left(x + 1\right) \left(x^{2} - x + 1\right)}$$
1/((1 + x)*(1 + x^2 - x))