### 2.28.9 Partial fraction expansion : `partfrac`

`partfrac` takes as argument a rational fraction.
`partfrac` returns the partial fraction expansion of this rational fraction.
The `partfrac` command is equivalent to the `convert` command with `parfrac` (or `partfrac` or `fullparfrac`) as option (see also 2.21.23).
Example :
Find the partial fraction expansion of :

x5−2x3+1
x4−2x3+2x2−2x+1

Input :

`partfrac((x```^```5-2*x```^```3+1)/(x```^```4-2*x```^```3+2*x```^```2-2*x+1))`

Output in real mode :

`x+2-1/(2*(x-1))+(x-3)/(2*(x```^```2+1))`

Output in complex mode:

`x+2+(-1+2*i)/((2-2*i)*((i)*x+1))+1/(2*(-x+1))+`
`(-1-2*i)/((2-2*i)*(x+i))`