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Simplifying Rational Expressions quiz

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  • What is a rational expression?
    A rational expression is a quotient of two polynomials, similar to how a rational number is a quotient of two integers.
  • What must you check in the denominator of a rational expression before simplifying?
    You must ensure the denominator is not zero, as division by zero makes the expression undefined.
  • How do you find where a rational expression is undefined?
    Set the denominator equal to zero and solve for the variable; these values make the expression undefined.
  • What is the first step in simplifying a rational expression?
    Factor the numerator and denominator completely.
  • After factoring, what do you do to simplify a rational expression?
    Cancel any common factors that appear in both the numerator and denominator.
  • What is the simplified form of 28x^3/35x^5?
    The simplified form is 4/(5x^2) after factoring and canceling common terms.
  • How do you evaluate a rational expression at a specific value?
    Substitute the value for the variable in both the numerator and denominator, then simplify.
  • What is the result of plugging x = 2 into x - 1 over 2x - 6?
    The result is -1/2.
  • What happens when you divide an expression by its opposite?
    You get -1 as the result, just like dividing a number by its opposite.
  • How can you recognize opposite factors in rational expressions?
    Opposite factors have every term with opposite signs, such as x + 4 and -x - 4.
  • What is the simplified result of 10 - x divided by x - 10?
    The simplified result is -1.
  • Are x + 3 and x - 3 considered opposite factors?
    No, they are conjugates, not opposites, because not all terms have opposite signs.
  • What is the simplified form of x - 5 over 3x^2 - 15x?
    The simplified form is 1/(3x) after factoring and canceling x - 5.
  • What should you do if the denominator is not fully factored?
    Factor it completely before attempting to cancel common factors.
  • How can you check if two expressions are opposites?
    Factor out a negative one from one expression and see if all terms match the other expression with opposite signs.