1. Partial Fractions Decomposition
Section 7.4
Precalculus PreAP/Dual, Revised ©2018
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§7.4: Partial Fractions Decomposition

2. §7.4: Partial Fractions Decomposition
Definitions
Consider adding two algebraic fractions Partial fraction decomposition reverses the process
2/28/2019 1:06 PM
§7.4: Partial Fractions Decomposition

3. §7.4: Partial Fractions Decomposition
Review
Solve 𝟑 𝒙−𝟑 − 𝟐 𝒙−𝟐
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§7.4: Partial Fractions Decomposition

4. §7.4: Partial Fractions Decomposition
Steps
Factor the denominator and exclude any repeating denominators
Separate the numerator by establishing 𝑨, 𝑩, etc…
Plug in missing values to solve
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§7.4: Partial Fractions Decomposition

5. §7.4: Partial Fractions Decomposition
Example 1
Write the partial fraction decomposition of 𝒙 𝒙 𝟐 −𝟓𝒙+𝟔
2/28/2019 1:06 PM
§7.4: Partial Fractions Decomposition

6. §7.4: Partial Fractions Decomposition
Example 1
Write the partial fraction decomposition of 𝒙 𝒙 𝟐 −𝟓𝒙+𝟔
2/28/2019 1:06 PM
§7.4: Partial Fractions Decomposition

7. §7.4: Partial Fractions Decomposition
Example 2
Write the partial fraction decomposition of 𝒙+𝟕 𝒙 𝟐 −𝒙−𝟔
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§7.4: Partial Fractions Decomposition

8. §7.4: Partial Fractions Decomposition
Your Turn
Write the partial fraction decomposition of 𝟐 𝒙 𝟐 −𝟏
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§7.4: Partial Fractions Decomposition

9. §7.4: Partial Fractions Decomposition
Process
Given 𝒇 𝒙 = 𝑷(𝒙 𝒙−𝒓 𝒏
Where polynomial 𝑷 𝒙 has degree < 𝒏
𝑷 𝒓 ≠𝟎
B. Then 𝒇 𝒙 can be decomposed with this cascading form
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§7.4: Partial Fractions Decomposition

10. §7.4: Partial Fractions Decomposition
Example 3
Write the partial fraction decomposition of 𝒙+𝟐 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝒙
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§7.4: Partial Fractions Decomposition

11. §7.4: Partial Fractions Decomposition
Example 3
Write the partial fraction decomposition of 𝒙+𝟐 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝒙
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§7.4: Partial Fractions Decomposition

12. §7.4: Partial Fractions Decomposition
Example 4
Write the partial fraction decomposition of 𝟕𝒙 𝟐 +𝟓𝒙+𝟐𝟑 𝒙+𝟏 𝒙 𝟐 +𝟒
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§7.4: Partial Fractions Decomposition

13. §7.4: Partial Fractions Decomposition
Example 4
Write the partial fraction decomposition of 𝟕𝒙 𝟐 +𝟓𝒙+𝟐𝟑 𝒙+𝟏 𝒙 𝟐 +𝟒
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§7.4: Partial Fractions Decomposition

14. §7.4: Partial Fractions Decomposition
Your Turn
Write the partial fraction decomposition of 𝒙 𝟐 −𝒙+𝟐 𝒙 𝒙+𝟐 𝟐
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§7.4: Partial Fractions Decomposition

15. §7.4: Partial Fractions Decomposition
Assignment
Page all, odd
2/28/2019 1:06 PM
§7.4: Partial Fractions Decomposition