mathjs/docs/reference/functions/rationalize.md

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 na object {Object} {Expression Node} expression: node simplified expression {Expression Node} numerator: simplified numerator of expression {Expression Node

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]

See also

simplify