SECTION 8-5Partial Fraction

Rational Expressions: Find a common denominator

1.

4

1

3

2

xx

2.

43

53

xx

x

Use partial fractions to decompose a rational function into Linear Factors

Guidelines for partial fraction decomposition

1. Factor the denominator

2. Assume there are constants A,B and C

3. Find a common denominator and then cancel the denominator

4. Because the resulting equation is true for all x, substitute convenient values x

5. Solve for A, B and C

3. 1072 xx

dx

4.

dxxxx

x

2821

22

Assignment• Page 561 # 1, 4, 5, ( decompose into partial fractions)• # 7, 9, and 13 (integrate)