ExpandDenominator
ExpandDenominator[expr]
expands out products and powers that appear as denominators in expr.
Details and Options
- ExpandDenominator works only on negative integer powers.
- ExpandDenominator applies only to the top level in expr.
- ExpandDenominator automatically threads over lists, as well as equations, inequalities, and logic functions.
- ExpandDenominator takes the following options:
-
Modulus 0 modulus to assume for integers Trig False whether to do trigonometric as well as algebraic transformations
Examples
open all close allBasic Examples (2)
Scope (6)
Expand the denominator of a rational function:
ExpandDenominator[(x - y) ^ 2 / (u - v) ^ 2]ExpandDenominator threads over sums:
ExpandDenominator[x / (a + b) ^ 2 + y / ((c + d)(c - d))]ExpandDenominator threads over Boolean combinations of equations and inequalities:
ExpandDenominator[x == c / (a + b) ^ 2 && y ≥ c / (a - b) ^ 2]Expand a denominator involving complex coefficients:
ExpandDenominator[(1 - x ^ 2) / ((x + I)(x - I))]Expand the denominator over the integers modulo 
:
ExpandDenominator[z / (2x + 3y) ^ 6, Modulus -> 4]Expand the denominator using expansion formulas for trigonometric functions:
ExpandDenominator[(a - b) / (Sin[2x] + 1), Trig -> True]Options (2)
Modulus (1)
Applications (2)
f = 1 / (3 x + 4) - 4 / (x + 2)ExpandDenominator[Together[f]]Verify that two expressions are equal:
expr1 = (x^6 - 1/(-1 + x^2)^3);expr2 = (-1 + x^6/-1 + 3 x^2 - 3 x^4 + x^6);expr1 == expr2Use ExpandDenominator to show that the equality is true:
ExpandDenominator[%]Properties & Relations (5)
ExpandDenominator leaves the numerator unexpanded:
ExpandDenominator[(a + b)(a - b) / ((c + d)(c - d))]ExpandNumerator expands the numerator, leaving the denominator unexpanded:
ExpandNumerator[(a + b)(a - b) / ((c + d)(c - d))]Expand expands the numerator and expands the fraction into a sum of fractions:
Expand[(a + b)(a - b) / ((c + d)(c - d))]ExpandAll expands the numerator, the denominator, and the fraction:
ExpandAll[(a + b)(a - b) / ((c + d)(c - d))]Use Factor, Numerator, and Denominator to factor the denominator back:
Numerator[#] / Factor[Denominator[#]]&[(a ^ 2 - b ^ 2) / (c ^ 2 - d ^ 2)]Text
Wolfram Research (1988), ExpandDenominator, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandDenominator.html (updated 2007).
CMS
Wolfram Language. 1988. "ExpandDenominator." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/ExpandDenominator.html.
APA
Wolfram Language. (1988). ExpandDenominator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExpandDenominator.html