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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 over the common denominator.
  • When adding 5/18 and 1/18, what do you do with the numerators and denominators?
    Add the numerators (5 + 1) and keep the denominator the same (18).
  • Why is it important to simplify your final answer when adding or subtracting rational expressions?
    Simplifying ensures the answer is in its simplest form and may involve canceling common factors.
  • What must you remember to do when subtracting rational expressions?
    Distribute the negative sign to all terms in the numerator of the second expression.
  • How do you simplify 6/18x?
    Factor both numerator and denominator, cancel common factors, and the answer is 1/3x.
  • What is the result of adding 5/18x and 1/18x?
    The result is 6/18x, which simplifies to 1/3x.
  • What is the common denominator in the expression x²/(x-1) - (–x+2)/(x-1)?
    The common denominator is x - 1.
  • How do you combine the numerators when subtracting x²/(x-1) – (–x+2)/(x-1)?
    Subtract the entire numerator of the second fraction from the first, distributing the negative sign.
  • After distributing the negative in x² – (–x + 2), what is the new numerator?
    The new numerator is x² + x – 2.
  • How do you factor x² + 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 to common factors in the numerator and denominator when simplifying rational expressions?
    Common factors are canceled out to further simplify the expression.
  • What is the simplified form of (x–1)(x+2)/(x–1)?
    The simplified form is x + 2.
  • Why is factoring quadratics important when simplifying rational expressions?
    Factoring helps identify and cancel common factors, leading to the simplest form.
  • What is the general strategy for adding or subtracting rational expressions with common denominators?
    Combine the numerators, keep the denominator, and simplify the result.
  • What should you always check for after combining rational expressions?
    Always check if the expression can be simplified further by factoring and canceling common factors.