NumeratorDenominator
NumeratorDenominator[expr]
gives the list {Numerator[expr],Denominator[expr]} of expr.
Details and Options
- Numerator picks out terms that do not have superficially negative exponents. Denominator picks out the remaining terms.
- An exponent is "superficially negative" if it has a negative number as a factor.
- The standard representation of rational expressions as products of powers means that you cannot simply use Part to extract numerators.
- NumeratorDenominator can be used on rational numbers.
- NumeratorDenominator automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Scope (7)
Select terms with syntactically positive and negative exponents:
Reconstruct the original expression:
NumeratorDenominator automatically threads over lists:
Compute the numerator and denominator over the integers modulo 5:
Compute the numerator and denominator while incorporating common trigonometric identities:
Options (2)
Applications (2)
Compute the numerator and denominator with respect to a specified modulus:
Compute the limit at infinity of a rational function:
Extract the numerator and denominator:
Apply Exponent to find the degree of the numerator and denominator:
We can see that the denominator has a larger degree. Thus, the function approaches zero as 
grows large:
This can be confirmed using Limit:
Text
Wolfram Research (2019), NumeratorDenominator, Wolfram Language function, https://reference.wolfram.com/language/ref/NumeratorDenominator.html.
CMS
Wolfram Language. 2019. "NumeratorDenominator." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NumeratorDenominator.html.
APA
Wolfram Language. (2019). NumeratorDenominator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NumeratorDenominator.html