Documentation

# `denom`

Denominator of a rational expression

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## Syntax

```denom(`f`)
```

## Description

`denom(f)` returns the denominator of the expression `f`.

`denom` regards the input as a rational expression: non-rational subexpressions such as `sin(x)`, `x^(1/2)` etc. are internally replaced by “temporary variables”. The denominator of this rationalized expression is computed, the temporary variables are finally replaced by the original subexpressions.

### Note

Numerator and denominator are not necessarily cancelled: the denominator returned by `denom` may have a non-trivial `gcd` with the numerator returned by `numer`. Pre-process the expression by `normal` to enforce cancellation of common factors. Cf. Example 2.

## Examples

### Example 1

We compute the denominators of some expressions:

`denom(-3/4)`
` `
`denom(x + 1/(2/3*x -2/x))`
` `
`denom((cos(x)^2 -1)/(cos(x) -1))`
` `

### Example 2

`denom` performs no cancellations if the rational expression is of the form “numerator/denominator”:

`r := (x^2 - 1)/(x^3 - x^2 + x - 1): denom(r)`
` `

This denominator has a common factor with the numerator of `r`; `normal` enforces cancellation of common factors:

`denom(normal(r))`
` `

However, automatic normalization occurs if the input expression is a sum:

`denom(r + x/(x + 1) + 1/(x + 1) - 1)`
` `
`delete r:`

## Parameters

 `f`

## Return Values

Arithmetical expression.

`f`