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Adding and Subtracting Rational Expressions with Different Denominators definitions

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  • Rational Expression
    A fraction where both the numerator and denominator are polynomials, often requiring simplification or combination.
  • Least Common Denominator
    The smallest expression that is a multiple of each denominator, found by factoring and multiplying unique factors.
  • Equivalent Expression
    A rewritten form that has the same value as the original, often achieved by multiplying by missing factors.
  • Numerator
    The top part of a fraction or rational expression, which is combined or simplified during operations.
  • Denominator
    The bottom part of a fraction or rational expression, which must be the same to add or subtract.
  • Binomial
    A polynomial with exactly two terms, such as x+4 or x-8, often found in denominators.
  • Missing Factor
    A component needed to create a common denominator, used to adjust numerators and denominators.
  • Common Denominator
    A shared denominator that allows rational expressions to be added or subtracted directly.
  • Factoring
    The process of breaking down expressions into products of simpler expressions, essential for finding denominators.
  • Simplification
    The process of reducing an expression to its most basic form by combining like terms and distributing.
  • Like Terms
    Terms with the same variable parts, which can be combined to simplify expressions.
  • Coefficient
    A numerical factor multiplied by a variable in a term, important when distributing or combining terms.
  • Polynomial
    An algebraic expression made up of terms with variables raised to whole-number powers.
  • Standard Form
    An arrangement of a polynomial with terms ordered by descending degree, aiding in clarity and simplification.
  • Degree
    The highest power of the variable in a polynomial, which helps determine the complexity of expressions.