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Rational Equations definitions

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  • Rational Equation
    An equation containing a variable in the denominator, requiring special steps to solve and avoid undefined values.
  • Denominator
    The bottom part of a fraction, whose value must never be zero to prevent undefined expressions.
  • Restriction
    A value that makes the denominator zero, disqualifying it as a possible solution for the equation.
  • Least Common Denominator
    The smallest expression that all denominators share, used to clear fractions from an equation.
  • Linear Equation
    An equation with no variables in the denominator, often resulting after clearing fractions in rational equations.
  • Fraction
    A numerical expression with a numerator and denominator, often present in rational equations.
  • Solution
    A value for the variable that makes the equation true, provided it does not violate any restrictions.
  • Empty Set
    A result indicating no valid solution exists, often when the solution matches a restriction.
  • Variable
    A symbol representing an unknown value, frequently found in denominators of rational equations.
  • Term
    A single mathematical expression, such as a number or variable, within an equation.
  • Coefficient
    A numerical factor multiplying a variable in an equation, important when simplifying linear forms.
  • Standard Form
    A way of writing equations with variables and constants arranged for easier solving.
  • Constant
    A fixed value in an equation, often separated from variable terms during solving.
  • Parenthesis
    Symbols used to group expressions, requiring distribution when simplifying equations.
  • Distribution
    The process of multiplying a term across grouped expressions, essential for simplifying equations.