# numden

Extract numerator and denominator

## Syntax

• ```[N,D] = numden(A)``` example

## Description

example

``````[N,D] = numden(A)``` converts `A` to a rational form where the numerator and denominator are relatively prime polynomials with integer coefficients. The function returns the numerator and denominator of the rational form of an expression.If `A` is a symbolic or a numeric matrix, then `N` is the symbolic matrix of numerators, and `D` is the symbolic matrix of denominators. Both `N` and `D` are matrices of the same size as `A`.```

## Examples

### Numerators and Denominators of Symbolic Numbers

Find the numerator and denominator of a symbolic number.

`[n, d] = numden(sym(4/5))`
```n = 4 d = 5```

### Numerators and Denominators of Symbolic Expressions

Find the numerator and denominator of the symbolic expression.

```syms x y [n,d] = numden(x/y + y/x)```
```n = x^2 + y^2 d = x*y```

### Numerators and Denominators of Matrix Elements

Find the numerator and denominator of each element of a symbolic matrix.

```syms a b [n,d] = numden([a/b, 1/b; 1/a, 1/(a*b)])```
```n = [ a, 1] [ 1, 1] d = [ b, b] [ a, a*b]```

## Input Arguments

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### `A` — Inputsymbolic number | symbolic expression | symbolic function | symbolic vector | symbolic matrix

Input, specified as a symbolic number, expression, function, vector, or matrix.

## Output Arguments

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### `N` — Numeratorsymbolic number | symbolic expression | symbolic function | symbolic vector | symbolic matrix

Numerator, returned as a symbolic number, expression, function, vector, or matrix.

### `D` — Denominatorsymbolic number | symbolic expression | symbolic function | symbolic vector | symbolic matrix

Denominator, returned as a symbolic number, expression, function, vector, or matrix.