DivideSides [rel,x]
divides each side of the equation or inequality rel by x.
DivideSides [rel1,rel2]
divides the corresponding sides of two equations or inequalities.
DivideSides [rel]
divides each side of rel by the right-hand side, producing a 1 right-hand side.
DivideSides
DivideSides [rel,x]
divides each side of the equation or inequality rel by x.
DivideSides [rel1,rel2]
divides the corresponding sides of two equations or inequalities.
DivideSides [rel]
divides each side of rel by the right-hand side, producing a 1 right-hand side.
Details and Options
- The relations rel can have any of the following forms:
-
lhs==rhs equationslhs!=rhs inequationslhs>rhs or lhs>=rhs inequalitiesab>c≥… generalized inequalities
- The following options can be given:
-
TimeConstraint 30 time allowed for simplifying conditions
- Possible settings for GenerateConditions include:
-
Automatic return a condition only if it is not generically satisfiedTrue return any condition that is neededFalse never return any needed conditionsNone return unevaluated if conditions are needed
Examples
open all close allBasic Examples (4)
Divide both sides of an equation by 3:
DivideSides[3x == 21, 3]Divide both sides of an equation by the right-hand side:
DivideSides[a b == 3]Divide the corresponding sides of two equations:
DivideSides[a == b, c == d]Divide both sides of an inequality by the number b:
DivideSides[b x > 7, b]Scope (6)
Divide each side of an equation with three expressions by the rightmost side:
DivideSides[(Sin[a]/a) == (Sin[b]/b) == (Sin[c]/c)]Combine an equation and an inequation:
DivideSides[a ≠ b, c == d]Combine an equation and an inequality:
DivideSides[y > m x + b, z == 7]Divide each part of an generalized inequality by :
DivideSides[a == b > -5 > c, -5]Divide by a relations expressed using Piecewise :
DivideSides[Piecewise[{{x^2 == a*x + b, a > 1}, {x^2 <= a*x + b, True}}], a]Divide by the right-hand side both sides of an equation inside ConditionalExpression :
DivideSides[ConditionalExpression[(a/c) == (b/d), c ≠ 0]]Options (3)
Assumptions (1)
Place assumptions on variables to simplify results:
DivideSides[a x ^ 2 > b x + c, a, Assumptions -> a > 0]By default, the different cases will be returned:
MultiplySides[a x ^ 2 > b x + c, 1 / a]GenerateConditions (2)
The default setting GenerateConditions ->All creates a Piecewise expression if needed:
DivideSides[a b > c, b]GenerateConditions ->True returns a valid result with the needed condition:
DivideSides[ a b > c, b, GenerateConditions -> True]GenerateConditions False returns a valid result without the needed condition:
DivideSides[a b > c, b, GenerateConditions -> False]GenerateConditions None will fail if conditions are needed:
DivideSides[a / b > c, b, GenerateConditions -> None]GenerateConditions ->Automatic returns conditions that are not generically satisfied:
DivideSides[a x > b, GenerateConditions -> Automatic]If the condition only fails for a single point, it is not returned:
DivideSides[a x == b, GenerateConditions -> Automatic]DivideSides[a x == b, GenerateConditions -> True]Applications (1)
Derive the quadratic formula:
quadratic = a x^2 + b x + c == 0Multiply both sides by 4 a:
MultiplySides[quadratic, 4a, Assumptions -> a ≠ 0]//ExpandAdd b^2-4 a c to both sides:
AddSides[%, b^2 - 4a c]Factor the left-hand side:
Factor[%]Take the positive square root of both sides:
ApplySides[Sqrt, %]Cancel the square root of the square:
PowerExpand[%]Subtract b from both sides:
SubtractSides[%, b]Divide both sides by 2 a to obtain the quadratic formula for x with positive square root:
DivideSides[%, 2a, Assumptions -> a ≠ 0]Properties & Relations (5)
True and False are considered trivial equations:
DivideSides[True, a]DivideSides[1 == 0, a]DivideSides transforms equations to equivalent equations:
DivideSides[3x == 15, 3]Solve gives values for the variables that make the equation true:
Solve[3x == 15, x]Reduce can be used to rewrite an equation in the form var==value:
Reduce[3x == 15, x]Simplify includes the functionality of DivideSides :
Simplify[2x == 2a b + 4b]DivideSides[2x == 2a b + 4b, 2]Using Expand to multiply out terms on each side of the equations:
DivideSides[3x == 15 - 21y, 3]%//ExpandDivideSides [eq,x] is the inverse of MultiplySides [eq,x]:
DivideSides[2x == 24 - 4y, 2]MultiplySides[x == (1/2) (24 - 4 y), 2]Related Guides
History
Text
Wolfram Research (2018), DivideSides, Wolfram Language function, https://reference.wolfram.com/language/ref/DivideSides.html.
CMS
Wolfram Language. 2018. "DivideSides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DivideSides.html.
APA
Wolfram Language. (2018). DivideSides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DivideSides.html
BibTeX
@misc{reference.wolfram_2026_dividesides, author="Wolfram Research", title="{DivideSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/DivideSides.html}", note=[Accessed: 16-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_dividesides, organization={Wolfram Research}, title={DivideSides}, year={2018}, url={https://reference.wolfram.com/language/ref/DivideSides.html}, note=[Accessed: 16-August-2026]}