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Adding and Subtracting Rational Expressions with Common Denominators quiz

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  • What is the first step when adding or subtracting rational expressions with common denominators?
    Combine the numerators and keep the denominator the same.
  • What must you always do after combining rational expressions?
    You must always simplify your final answer.
  • How do you simplify a rational expression after combining numerators?
    Factor the numerator and denominator, then cancel any common factors.
  • What should you do with the negative sign when subtracting rational expressions?
    Distribute the negative sign to all terms in the numerator of the second fraction.
  • What is the common denominator in the expression x^2/(x-1) - (-x+2)/(x-1)?
    The common denominator is x-1.
  • How do you factor the quadratic x^2 + x - 2?
    Find two numbers that multiply to -2 and add to 1; these are -1 and 2, so it factors to (x-1)(x+2).
  • What happens when you have the same factor in both the numerator and denominator?
    You can cancel the common factor from both the numerator and denominator.
  • What is the simplified result of x^2/(x-1) - (-x+2)/(x-1)?
    The simplified result is x+2.
  • When adding 5/18 + 1/18, what is the result before simplification?
    The result is 6/18.
  • How do you simplify 6/18?
    Factor both numbers and cancel common factors to get 1/3.
  • What is the result of adding 5/(18x) + 1/(18x)?
    The result is 6/(18x).
  • How do you simplify 6/(18x)?
    Factor 6 and 18, cancel common factors, and the simplified answer is 1/(3x).
  • What is the importance of factoring polynomials when simplifying rational expressions?
    Factoring helps identify and cancel common factors, leading to a simpler expression.
  • What should you always check for after combining rational expressions?
    Always check if the numerator and denominator can be factored and simplified further.
  • What is the strategy for adding or subtracting rational expressions with common denominators?
    Combine the numerators, keep the denominator, and then simplify the result.