# simplifyFraction

Simplify symbolic rational expressions

## Syntax

``simplifyFraction(expr)``
``simplifyFraction(expr,'Expand',true)``

## Description

example

````simplifyFraction(expr)` simplifies the rational expression `expr` such that the numerator and denominator have no divisors in common.```

example

````simplifyFraction(expr,'Expand',true)` expands the numerator and denominator of the resulting simplified fraction as polynomials without factorization.```

## Examples

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Simplify two rational expressions by using `simplifyFraction`.

```syms x y fraction = (x^2-1)/(x+1); simplifyFraction(fraction)```
```ans = x - 1```
```fraction = (y*(x^2-1))/((x+1)*(x-1)); simplifyFraction(fraction)```
```ans = y```

Create a rational expression. Simplify the expression by using `simplifyFraction`.

```syms x y fraction = ((y+1)^2*(x^2-1))/((x+1)*(x-1)^2); simplifyFraction(fraction)```
```ans = (y + 1)^2/(x - 1)```

Simplify the same rational expression again. Expand the numerator and denominator of the resulting fraction by setting `'Expand'` to `true`.

`simplifyFraction(fraction,'Expand',true)`
```ans = (y^2 + 2*y + 1)/(x - 1)```

Simplify rational expressions by using `simplifyFraction`.

```syms x expr = ((x^2+2*x+1)/(x+1))^(1/2); simplifyFraction(expr)```
```ans = (x + 1)^(1/2)```

Simplify rational expressions that contain irrational subexpressions instead of variables.

```expr = (1-sin(x)^2)/(1-sin(x)); simplifyFraction(expr)```
```ans = sin(x) + 1```

`simplifyFraction` does not apply algebraic identities to simplify the rational expression. Show that `simplifyFraction` does not apply standard trigonometric identities.

```expr = (1-cos(x)^2)/sin(x); simplifyFraction(expr)```
```ans = -(cos(x)^2 - 1)/sin(x)```

## Input Arguments

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

## Tips

• `expr` can contain irrational subexpressions, such as `sin(x)` and `x^(-1/3)`. `simplifyFraction` simplifies such expressions as if they were variables.

• `simplifyFraction` does not apply algebraic identities.

## Alternatives

You can also simplify rational expressions using the general simplification function `simplify`. However, `simplifyFraction` is more efficient for simplifying rational expressions.

Introduced in R2011b

## Support

#### Mathematical Modeling with Symbolic Math Toolbox

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