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Rational Equations definitions

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  • Rational Equation
    An equation containing variables in the denominator of one or more fractions, requiring special steps to solve.
  • Denominator
    The bottom part of a fraction, whose value cannot be zero in rational equations.
  • Restriction
    A value for a variable that would make a denominator zero, and thus is excluded from possible solutions.
  • Least Common Denominator
    The smallest expression that is a common multiple of all denominators in a rational equation.
  • Linear Equation
    An equation of the first degree, often resulting from clearing denominators in a rational equation.
  • Solution Set
    The collection of all values that satisfy a given equation, possibly empty if restrictions are violated.
  • Empty Set
    A set containing no elements, representing no valid solutions for an equation.
  • Fraction
    A numerical quantity expressed as one number divided by another, often present in rational equations.
  • Variable
    A symbol, typically x, representing an unknown value in an equation.
  • Constant
    A fixed value in an equation, not affected by the variable.
  • Distribution
    The process of multiplying a term across terms inside parentheses, used when clearing denominators.
  • Like Terms
    Terms in an equation that have the same variable raised to the same power and can be combined.
  • Isolating x
    The process of rearranging an equation to have the variable x alone on one side.
  • Parenthesis
    Symbols used to group terms, especially important when distributing or combining terms.
  • Numerator
    The top part of a fraction, representing the number being divided by the denominator.