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Adding and Subtracting Rational Expressions with Common Denominators definitions

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  • Rational Expression
    A fraction where both numerator and denominator are polynomials, often requiring simplification and factoring.
  • Common Denominator
    A shared denominator between two or more rational expressions, allowing numerators to be combined directly.
  • Numerator
    The top part of a rational expression, which is combined or simplified when adding or subtracting.
  • Denominator
    The bottom part of a rational expression, kept unchanged when combining expressions with the same value.
  • Simplification
    The process of reducing a rational expression to its most basic form by canceling common factors.
  • Factoring
    Breaking down a polynomial into products of simpler expressions, often used to reveal common factors.
  • Prime Factor
    A basic building block of a number or expression, used to simplify numerators and denominators.
  • Quadratic
    A polynomial of degree two, often requiring factoring to simplify rational expressions.
  • Trinomial
    A polynomial with three terms, commonly encountered when factoring numerators in rational expressions.
  • Coefficient
    A numerical value multiplying a variable in a polynomial, important for combining and simplifying terms.
  • Polynomial
    An algebraic expression consisting of terms with variables and coefficients, forming numerators and denominators.
  • Exponent
    A value indicating repeated multiplication of a variable, often seen in terms like x squared.
  • Term
    A single part of a polynomial, separated by addition or subtraction, combined when adding or subtracting expressions.
  • Negative Sign
    A symbol distributed across terms in subtraction, affecting the outcome when combining numerators.
  • Polynomial Division
    A process used to simplify rational expressions, often after factoring and canceling common factors.