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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 simplified by factoring and canceling common factors.
  • Common Denominator
    A shared polynomial in the denominators of two or more rational expressions, allowing for direct addition or subtraction.
  • Numerator
    The top part of a rational expression, which is combined when adding or subtracting expressions with like denominators.
  • Denominator
    The bottom part of a rational expression, kept unchanged when combining expressions with the same denominator.
  • Simplification
    The process of reducing a rational expression to its simplest form by factoring and canceling common factors.
  • Factoring
    Breaking down a polynomial into products of simpler polynomials, often used to simplify rational expressions.
  • Quadratic
    A polynomial of degree two, commonly encountered in numerators when simplifying rational expressions.
  • Prime Factor
    A basic building block of numbers or polynomials, used to break down numerators and denominators for simplification.
  • Coefficient
    A numerical value multiplying a variable in a polynomial, important for identifying terms during factoring.
  • Term
    A single part of a polynomial, separated by addition or subtraction, crucial when distributing negatives in subtraction.
  • Degree
    The highest power of the variable in a polynomial, used to identify the type of expression being simplified.
  • Distribution
    Applying a negative sign to each term in a polynomial, especially important when subtracting rational expressions.
  • Cancellation
    Eliminating common factors from both numerator and denominator to achieve a simpler rational expression.
  • Variable
    A symbol representing an unknown value, present in both numerators and denominators of rational expressions.
  • Polynomial
    An algebraic expression consisting of terms with variables and coefficients, forming the basis of rational expressions.