5017 Partial Fractions AP Calculus

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

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.

Examples: Linear factors Example 1: Linear factors

Examples: Linear factors Example 2: Linear factors

Logistic Growth

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

Examples: Repeated Linear factors Example 4: Repeated Linear Factors

Examples: Quadratic Factors Example 5:

Examples: Quadratic Factors Example 6:

Examples: Quadratic Factors Example 7:

Last Update: 03/08/10