# 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 #

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

### Parameters #

Parameter Type Description
`expr` Node | string The expression to check if is a polynomial expression
`optional` Object | 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 | Node The rational polynomial of `expr` or an object `{expression, numerator, denominator, variables, coefficients}`, where `expression` is a `Node` with the node simplified expression, `numerator` is a `Node` with the simplified numerator of expression, `denominator` is a `Node` or `boolean` with the simplified denominator or `false` (if there is no denominator), `variables` is an array with variable names, and `coefficients` is an array with coefficients of numerator sorted by increased exponent {Expression Node} node simplified expression

### Throws #

Type | Description —- | ———–

## Examples #

``````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]
``````