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>cgeneralized inequalities
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    GenerateConditionsAllwhether 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

open allclose all

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]:

Introduced in 2018
 (11.3)