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Simplifying Rational Expressions definitions

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  • Rational Expression
    A fraction where both the numerator and denominator are polynomials, similar to rational numbers but with variables.
  • Numerator
    The top part of a fraction or rational expression, representing the dividend in the division.
  • Denominator
    The bottom part of a fraction or rational expression, representing the divisor and must not be zero.
  • Polynomial
    An algebraic expression made up of terms consisting of numbers and variables combined by addition, subtraction, or multiplication.
  • Factor
    A number or expression that divides another exactly, used to break down polynomials for simplification.
  • Common Factor
    A shared number or expression in both the numerator and denominator that can be canceled to simplify.
  • Undefined Expression
    A rational expression where the denominator equals zero, making the value impossible to determine.
  • Lowest Terms
    A form of a rational expression where all common factors have been canceled, leaving the simplest version.
  • Greatest Common Factor
    The largest factor shared by all terms in a polynomial, useful for factoring and simplifying.
  • Conjugate
    A pair of expressions in the form a+b and a−b, which are not opposites but differ only in the sign between terms.
  • Opposite Factors
    Expressions where every term has the opposite sign, such as x−a and a−x, resulting in a simplification to negative one.
  • Prime Factorization
    Breaking down a number or expression into its smallest possible factors, often used before canceling.
  • Variable
    A symbol, usually a letter, representing an unknown value in algebraic expressions.
  • Coefficient
    A numerical factor multiplied by a variable in a term of a polynomial.
  • Fraction
    A numerical expression representing division, used as a model for rational expressions in algebra.