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

An expression to simplify:

The solution

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