# Python | sympy.apart() method

With the help of sympy.apart() method, we can performs a partial fraction decomposition on a rational mathematical expression.

Syntax: apart(expression)

Parameters:
expression – It is a rational mathematical expression.

Returns: Returns an expression after the partial decomposition.

Example #1:
In this example we can see that by using sympy.apart() method, we can get a partial fraction decomposition of a given mathematical expression.

 `# import sympy ` `from` `sympy ``import` `*` ` `  `x ``=` `symbols(``'x'``) ` `expr ``=` `(``4` `*` `x``*``*``3` `+` `21` `*` `x``*``*``2` `+` `10` `*` `x ``+` `12``) ``/` `(x``*``*``4` `+` `5` `*` `x``*``*``3` `+` `5` `*` `x``*``*``2` `+` `4` `*` `x) ` ` `  `print``(``"Mathematical expression : {}"``.``format``(expr)) ` `   `  `# Use sympy.apart() method ` `pd ``=` `apart(expr)  ` `   `  `print``(``"After Partial Decomposition : {}"``.``format``(pd))  `

Output:

```Mathematical expression : (4*x**3 + 21*x**2 + 10*x + 12)/(x**4 + 5*x**3 + 5*x**2 + 4*x)
After Partial Decomposition : (2*x - 1)/(x**2 + x + 1) - 1/(x + 4) + 3/x
```

Example #2:

 `# import sympy ` `from` `sympy ``import` `*`  ` `  `x ``=` `symbols(``'x'``) ` `expr ``=` `1``/``(x ``+` `3``)(x ``+` `2``) ` ` `  `print``(``"Mathematical expression : {}"``.``format``(expr)) ` `   `  `# Use sympy.factor_list() method ` `pd ``=` `apart(expr)  ` `   `  `print``(``"After Partial Decomposition : {}"``.``format``(pd))  `

Output:

```Mathematical expression : 1/((x + 2)*(x + 3))
After Partial Decomposition : -1/(x + 3) + 1/(x + 2)
```

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