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#### Search: #### Partfrac

Function: partfrac (<expr>, <var>) Expands the expression <expr> in partial fractions with respect to the main variable <var>. `partfrac` does a complete partial fraction decomposition. The algorithm employed is based on the fact that the denominators of the partial fraction expansion (the factors of the original denominator) are relatively prime. The numerators can be written as linear combinations of denominators, and the expansion falls out.

```          (%i1) 1/(1+x)^2 - 2/(1+x) + 2/(2+x);
2       2        1
(%o1)               ----- - ----- + --------
x + 2   x + 1          2
(x + 1)
(%i2) ratsimp (%);
x
(%o2)                 - -------------------
3      2
x  + 4 x  + 5 x + 2
(%i3) partfrac (%, x);
2       2        1
(%o3)               ----- - ----- + --------
x + 2   x + 1          2
(x + 1)```

```(%o1)                                true
(%i2) ```

### Related Examples

##### partfrac

f(x):=((3+x)+7)/((x^2...

'partfrac(f(x),x)=par...

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##### partfrac

partfrac((z^2+1)/((z-...

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##### partfrac

partfrac((4*x**3+11*x...

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##### partfrac

f(x):=1/x*(2*x^3+2*x^...

partfrac(f(x),x);

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##### partfrac

partfrac:((64*x^3+153...

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##### partfrac

partfrac((x-3)*(x-1)*...

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##### partfrac-ratsimp

f(x):=1/((x-1)*(1-k/x));

partfrac(f(x),x);

ratsimp(%);

Calculate

##### partfrac

f(x):=1/((x-a)*(x-b)^3);

partfrac(f(x),x);

Calculate

##### partfrac

partfrac((x**2+x-5)/(...

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##### partfrac

f(z):=(5*z^2 -8*z +5)...

partfrac(f(z),z);

Calculate 