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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) by factoring the denominators.
  • How do you create equivalent rational expressions when adding or subtracting?
    Multiply the numerator and denominator of each expression by the missing factor needed to reach the LCD.
  • What is the LCD of the denominators 30 and 20?
    The LCD is 60.
  • After finding the LCD, what is the next step in adding rational expressions?
    Rewrite each rational expression with the LCD as the denominator by multiplying by the missing factors.
  • 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 LCD for the denominators x+4 and x-8?
    The LCD is (x+4)(x-8).
  • How do you simplify the numerator after combining terms in rational expressions?
    Distribute coefficients and combine like terms in the numerator.
  • What is the result of adding 2x over 60x^2 and 3 over 60x^2?
    The result is (2x + 3) over 60x^2.
  • What do you multiply the numerator and denominator of 2/(x+4) by to get the LCD with x-8?
    Multiply by (x-8).
  • What do you multiply the numerator and denominator of 7/(x-8) by to get the LCD with x+4?
    Multiply by (x+4).
  • How do you write the subtraction of 2/(x+4) and 7/(x-8) as a single expression?
    Write as [2(x-8) - 7(x+4)] over (x+4)(x-8).
  • What is the simplified numerator when you distribute and combine 2(x-8) - 7(x+4)?
    The simplified numerator is -5x - 44.
  • What is the fully simplified rational expression for 2/(x+4) - 7/(x-8)?
    It is (-5x - 44) over (x+4)(x-8).
  • Why is understanding terms, coefficients, and polynomial degrees important in these operations?
    It helps in correctly distributing, combining like terms, and simplifying rational expressions.
  • What is the purpose of finding the LCD when adding or subtracting rational expressions?
    The LCD allows you to rewrite expressions with a common denominator so you can combine them.