5017 Partial Fractions AP Calculus
Dec 31, 2015
Partial Fractions
Remember: Adding Fractions Butterfly Method:
Decomposition: GIVEN: SUM FIND: ADDENDS ( Like Factoring- given the product (answer) want to find the problem)
a c
b d
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
2
Ax B
ax bx c
A
mx b
a. Convenient x-values.b. Equate the coefficients.
Examples: Repeated Linear factors
Example 3: Repeated Linear Factors
Must do all possibilities up to the given exponent.
3 2 3( 2) ( 2) ( 2) ( 2)
A B C
x x x x
2
3 2
5 20 6
2
x x
x x x