# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

# numden

Extract numerator and denominator

## Syntax

``````[N,D] = numden(A)``````

## 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

collapse all

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

## Output Arguments

collapse all

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

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