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How Do You Subtract Two Rational Expressions with Different Denominators?

Simplify the expression shown on the right.

Summary

  1. We are subtracting two rational expressions
  2. LCD stands for least common denominator
  3. The negative sign flips the signs of what is in the second parentheses

Notes

    1. Since the two denominators are not equal, we cannot add the numerators right away
    1. LCD stands for least common denominator
    1. x2-9 is a difference of squares and has a special method for factoring
    1. LCD stands for least common denominator
    1. The factor (x-3) shows up once in the first denominator and no times in the second denominator
    2. So the maximum number of time (x-3) shows up is 1
    3. The factor (x+3) shows up once in each denominator, so the maximum number of times it shows up is just 1
    1. LCD stands for least common denominator
    1. LCD stands for least common denominator
    1. LCD stands for least common denominator
    1. We multiplied the binomials (x-3) and (x+3) to get x2-9
    2. When we multiply two binomials together we have to FOIL them together
    1. LCD stands for least common denominator
    1. LCD stands for least common denominator
    1. LCD stands for least common denominator
    1. LCD stands for least common denominator
    1. Multiplying by one won't change the value of the fraction
    2. LCD stands for least common denominator
    1. The fancy form of one is (x-3) divided by (x-3)
    2. Multiplying by one won't change the value of the fraction
    3. LCD stands for least common denominator
    1. The trinomial x2+9x-36 comes from FOILing together (x+12) and (x-3)
    1. LCD stands for least common denominator
    1. A positive sign in front of a parentheses is the same as multiplying by positive 1, so the inside doesn't change
    1. A negative sign in front of a parentheses is the same as multiplying by -1, so the signs inside flip
    1. A negative sign in front of a parentheses is the same as multiplying by -1, so the signs inside flip
    1. LCD stands for least common denominator
    1. Like terms are terms with the same variables raised to the same power
    2. x-9x=-8x
    3. -5+36=31
    1. LCD stands for least common denominator
    1. LCD stands for least common denominator