1. 5017 Partial Fractions AP Calculus

2. Partial Fractions Remember: Adding FractionsButterfly Method: Decomposition: GIVEN: SUM FIND: ADDENDS ( Like Factoring- given the product (answer) want to find the problem)

3. Steps: ** Check if proper fraction Factor the denominator and write the addition problem. Write fraction addition problem using a numerator one degree less than the denominator; may have repeated factor. If a. Linear factors, use b. Quadratic factors, use 3. Add the new fraction; find LCD, etc. 4. Set numerators equal. 5. Solve a. Convenient x-values. b. Equate the coefficients.

4. Examples: Linear factors Example 1: Linear factors

5. Examples: Linear factors Example 2: Linear factors

6. Logistic Growth

7. Examples: Repeated Linear factors Example 3: Repeated Linear Factors Must do all possibilities up to the given exponent.

8. Examples: Repeated Linear factors Example 4: Repeated Linear Factors

9. Examples: Quadratic Factors Example 5:

10. Examples: Quadratic Factors Example 6:

11. Examples: Quadratic Factors Example 7:

12. Last Update: 03/08/10