mathjs/docs/reference/functions/rationalize.md

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# Function rationalize

Transform a rationalizable expression in a rational fraction.
If rational fraction is one variable polynomial then converts
the numerator and denominator in canonical form, with decreasing
exponents, returning the coefficients of numerator.


## Syntax

```js
rationalize(expr)
rationalize(expr, detailed)
rationalize(expr, scope)
rationalize(expr, scope, detailed)
```

### Parameters

Parameter | Type | Description
--------- | ---- | -----------
`expr` | Node &#124; string | The expression to check if is a polynomial expression
`optional` | Object &#124; boolean | scope of expression or true for already evaluated rational expression at input
`detailed` | Boolean | optional True if return an object, false if return expression node (default)

### Returns

Type | Description
---- | -----------
Object &#124; Expression Node | The rational polynomial of `expr` or na object {Object} {Expression Node} expression: node simplified expression {Expression Node} numerator: simplified numerator of expression {Expression Node | boolean} denominator: simplified denominator or false (if there is no denominator) {Array}           variables:  variable names {Array}           coefficients: coefficients of numerator sorted by increased exponent {Expression Node}  node simplified expression


## Examples

```js
math.rationalize('sin(x)+y')
              //  Error: There is an unsolved function call
math.rationalize('2x/y - y/(x+1)')
              // (2*x^2-y^2+2*x)/(x*y+y)
math.rationalize('(2x+1)^6')
              // 64*x^6+192*x^5+240*x^4+160*x^3+60*x^2+12*x+1
math.rationalize('2x/( (2x-1) / (3x+2) ) - 5x/ ( (3x+4) / (2x^2-5) ) + 3')
              // -20*x^4+28*x^3+104*x^2+6*x-12)/(6*x^2+5*x-4)
math.rationalize('x/(1-x)/(x-2)/(x-3)/(x-4) + 2x/ ( (1-2x)/(2-3x) )/ ((3-4x)/(4-5x) )') =
              // (-30*x^7+344*x^6-1506*x^5+3200*x^4-3472*x^3+1846*x^2-381*x)/
              //     (-8*x^6+90*x^5-383*x^4+780*x^3-797*x^2+390*x-72)

math.rationalize('x+x+x+y',{y:1}) // 3*x+1
math.rationalize('x+x+x+y',{})    // 3*x+y

const ret = math.rationalize('x+x+x+y',{},true)
              // ret.expression=3*x+y, ret.variables = ["x","y"]
const ret = math.rationalize('-2+5x^2',{},true)
              // ret.expression=5*x^2-2, ret.variables = ["x"], ret.coefficients=[-2,0,5]
```


## See also

[simplify](simplify.md)