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Adding and Subtracting Rational Expressions with Different Denominators definitions

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  • Rational Expression
    A fraction where both numerator and denominator are polynomials, often requiring simplification or manipulation.
  • Least Common Denominator
    The smallest shared multiple of denominators, found by factoring and multiplying all unique factors present.
  • Binomial
    An algebraic expression consisting of two distinct terms, often used in denominators for factoring.
  • Equivalent Expression
    A rewritten form of an expression that maintains the same value, achieved by multiplying by missing factors.
  • Missing Factor
    A component absent from a denominator, necessary for creating a common denominator in rational expressions.
  • Numerator
    The top part of a fraction or rational expression, combined or simplified during addition or subtraction.
  • Denominator
    The bottom part of a fraction or rational expression, often factored to find commonality for operations.
  • Polynomial
    An expression made up of terms with variables and coefficients, forming the basis of rational expressions.
  • Coefficient
    A numerical factor attached to a variable within a term, distributed and combined during simplification.
  • Like Terms
    Terms sharing identical variable parts, combined to simplify numerators in rational expressions.
  • Standard Form
    An arrangement of a polynomial or expression where terms are ordered by degree, aiding clarity and simplification.
  • Factoring
    The process of breaking down expressions into products of simpler components, essential for finding common denominators.
  • Distribution
    Applying a coefficient to each term inside parentheses, used to expand numerators before combining terms.
  • Simplification
    The process of reducing an expression to its most concise form, often after combining like terms and factoring.
  • Rational Number
    A number expressed as a fraction of two integers, serving as a model for operations with rational expressions.