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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.

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Presentation on theme: "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."— Presentation transcript:

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 partial fraction decomposition. 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(x 2 – 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! 16 1 –10 3 ↓ 6 67 7 –3 0 6x 2 + 7x – 3 6x 2 + 9x – 2x – 3 3x(2x + 3) – 1(2x + 3) (3x – 1)(2x + 3) denom = (x – 1)(3x – 1)(2x + 3) –18 7 –29

8 Ex 4) cont…

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

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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.

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Presentation on theme: "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."— Presentation transcript:

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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.

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Presentation on theme: "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."— Presentation transcript:

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