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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 + x^2))
$$- \frac{x + 2}{3 \left(x^{2} + x + 1\right)} + \frac{1}{3 \left(x - 1\right)}$$
    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 + x^2))