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==rhsequations
    lhs!=rhsinequations
    lhs>rhs or lhs>=rhs inequalities
    ab>c≥…generalized inequalities
  • The following options can be given:
  • Assumptions $Assumptionsassumptions on parameters
    GenerateConditions Allwhether to generate conditions on parameters
    TimeConstraint30time allowed for simplifying conditions
  • Possible settings for GenerateConditions include:
  • Allreturn all possible answers using Piecewise
    Automaticreturn a condition only if it is not generically satisfied
    Truereturn any condition that is needed
    Falsenever return any needed conditions
    Nonereturn unevaluated if conditions are needed

Examples

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Basic Examples  (4)

Divide both sides of an equation by 3:

Divide both sides of an equation by the right-hand side:

Divide the corresponding sides of two equations:

Divide both sides of an inequality by the number b:

Scope  (6)

Divide each side of an equation with three expressions by the rightmost side:

Combine an equation and an inequation:

Combine an equation and an inequality:

Divide each part of an generalized inequality by :

Divide by a relations expressed using Piecewise:

Divide by the right-hand side both sides of an equation inside ConditionalExpression:

Options  (3)

Assumptions  (1)

Place assumptions on variables to simplify results:

By default, the different cases will be returned:

GenerateConditions  (2)

The default setting GenerateConditions->All creates a Piecewise expression if needed:

GenerateConditions->True returns a valid result with the needed condition:

GenerateConditionsFalse returns a valid result without the needed condition:

GenerateConditionsNone will fail if conditions are needed:

GenerateConditions->Automatic returns conditions that are not generically satisfied:

If the condition only fails for a single point, it is not returned:

Applications  (1)

Derive the quadratic formula:

Multiply both sides by 4 a:

Add b^2-4 a c to both sides:

Factor the left-hand side:

Take the positive square root of both sides:

Cancel the square root of the square:

Subtract b from both sides:

Divide both sides by 2 a to obtain the quadratic formula for x with positive square root:

Properties & Relations  (5)

True and False are considered trivial equations:

DivideSides transforms equations to equivalent equations:

Solve gives values for the variables that make the equation true:

Reduce can be used to rewrite an equation in the form var==value:

Simplify includes the functionality of DivideSides:

Using Expand to multiply out terms on each side of the equations:

DivideSides[eq,x] is the inverse of MultiplySides[eq,x]:

Wolfram Research (2018), DivideSides, Wolfram Language function, https://reference.wolfram.com/language/ref/DivideSides.html.

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_2024_dividesides, author="Wolfram Research", title="{DivideSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/DivideSides.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_dividesides, organization={Wolfram Research}, title={DivideSides}, year={2018}, url={https://reference.wolfram.com/language/ref/DivideSides.html}, note=[Accessed: 21-December-2024 ]}