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7.8 Partial Fractions

7.8 Partial Fractions. If we wanted to add something like this:. We would need to find a common denominator!. Now, we want to REVERSE the process! Go from here,. to here!. This process is called partial fraction decomposition . Steps: (1) Factor the denominator

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7.8 Partial Fractions

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  1. 7.8 Partial Fractions

  2. If we wanted to add something like this: We would need to find a common denominator! Now, we want to REVERSE the process! Go from here, to here!

  3. This process is called partialfractiondecomposition. Steps: (1) Factor the denominator (2) Express as two (or more) fractions with A & B (or more) as placeholders for the numerators (3) Multiply both sides by LCD (4) Solve for A & B (or more) by letting x equal values that would make the other letter be multiplied by 0 (5) Substitute A & B (sometimes simple, sometimes not!)

  4. For all examples, decompose into partial fractions. Ex 1)

  5. Ex 2) x(x2 – 2x – 15)

  6. If (x – a)n is a factor of the denominator, you will need (x – a), (x – a)2, …, (x – a)n Ex 3) To solve for B, use A & C & let x = 0:

  7. Ex 4) Factor bottom! 1 6 1 –10 3 ↓ 6 7 –3 6 7 –3 0 • 6x2 + 7x – 3 • 6x2 + 9x – 2x – 3 • 3x(2x + 3) – 1(2x + 3) • (3x – 1)(2x + 3) • denom = (x – 1)(3x – 1)(2x + 3) –18 9 –2 7

  8. Ex 4) cont…

  9. Homework #708 Pg 378 #1, 5, 7, 18, 21, 29

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