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Adding and Subtracting Rational Expressions with Common Denominators definitions

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  • Rational Expression
    A fraction where both the numerator and denominator are polynomials, often involving variables.
  • Numerator
    The top part of a fraction or rational expression, representing the quantity being divided.
  • Denominator
    The bottom part of a fraction or rational expression, indicating the divisor or base.
  • Common Denominator
    A shared denominator among two or more rational expressions, allowing direct addition or subtraction.
  • Simplification
    The process of reducing an expression to its most basic or compact form by canceling common factors.
  • Factoring
    Breaking down a polynomial into products of simpler polynomials or numbers, often to reveal common factors.
  • Quadratic
    A polynomial of degree two, typically in the form ax² + bx + c, often requiring special factoring techniques.
  • Prime Factor
    A factor that cannot be broken down further except by one and itself, used to simplify expressions.
  • Standard Form
    An expression written in a conventional, simplified arrangement, often with terms ordered by degree.
  • Polynomial
    An algebraic expression made up of terms involving variables raised to whole-number powers and coefficients.
  • Coefficient
    A numerical factor multiplying a variable within a term of a polynomial or rational expression.
  • Term
    A single part of an expression, separated by plus or minus signs, which may include variables and coefficients.
  • Distribution
    Applying a sign or factor to each term within parentheses, such as spreading a negative across a sum.
  • Cancellation
    Eliminating common factors from the numerator and denominator to reduce a rational expression.
  • Variable
    A symbol, usually a letter, representing an unknown or changeable value within an expression.