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Adding and Subtracting Rational Expressions with Different Denominators quiz

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  • What is the first step when adding or subtracting rational expressions with different denominators?
    The first step is to find the least common denominator (LCD) of the rational expressions.
  • How do you find the LCD for rational expressions with binomial denominators?
    Factor each denominator and multiply together all unique factors to get the LCD.
  • What do you do after finding the LCD when adding rational expressions?
    Rewrite each rational expression with the LCD as the new denominator by multiplying by missing factors.
  • Why do you multiply the numerator and denominator by the missing factor?
    Multiplying by the missing factor creates equivalent rational expressions with the same denominator.
  • What is the LCD for the denominators 30x and 20x²?
    The LCD is 60x².
  • How do you combine the numerators once the denominators are the same?
    Add or subtract the numerators and keep the common denominator.
  • What is the result of adding 2x/30x and 3/20x² after rewriting with the LCD?
    The result is (2x + 3) / 60x².
  • How do you write 2/(x+4) and 7/(x-8) as a single rational expression?
    Multiply each by the missing factor to get a common denominator, then combine the numerators.
  • What is the LCD for denominators x+4 and x-8?
    The LCD is (x+4)(x-8).
  • What is the numerator after combining 2/(x+4) and 7/(x-8) with the LCD?
    The numerator is 2(x-8) - 7(x+4).
  • How do you simplify the numerator 2(x-8) - 7(x+4)?
    Distribute and combine like terms to get -5x - 44.
  • What is the fully simplified rational expression for 2/(x+4) - 7/(x-8)?
    The simplified expression is (-5x - 44) / [(x+4)(x-8)].
  • Why is it important to factor denominators when finding the LCD?
    Factoring ensures you include all unique factors needed for the LCD.
  • What should you do if the numerators cannot be combined further after addition or subtraction?
    Leave the numerators as they are and write the final expression over the common denominator.
  • What algebraic concepts are reinforced when adding and subtracting rational expressions?
    This process reinforces understanding of polynomials, terms, coefficients, and exponents.