Transcript
Section 5.3Partial Fractions
The Idea Behind Partial Fraction Decomposition
Each of the two fractions on the right is called a partial fraction. The sum of these fractions is called the partial fraction decomposition of the rational expression on the left-hand side.
The Partial Fraction Decomposition of a Rational Expression with Distinct Linear Factors in the
Denominator
Example
Find the partial fraction decomposition of
6 14
3 5
x
x x
The Partial Fraction Decomposition of a Rational Expression with Linear Factors in the Denominator, Some of
Which are Repeated
Example
2
Find the partial fraction decomposition
8
( 2)
x
x x
The Partial Fraction Decomposition of a Rational Expression with Prime,
Nonrepeated Quadratic Factors in the Denominator
Graphing Calculator
Example
2
2
Find the partial fraction decomposition of
3 4 2
2 3 5
x x
x x x
The Partial Fraction Decomposition of a Rational Expression with a
Prime, Repeated Quadratic Factor in the Denominator
Example
3
22
Find the partial fraction decomposition of
2 1
2
x x
x
(a)
(b)
(c)
(d)
Find the partial fraction decomposition of
14
2 5
x
x x
4 3
2 52 3
2 51 3
2 54 2
2 5
x x
x x
x x
x x
(a)
(b)
(c)
(d)
2
Find the partial fraction decomposition of
2 11
( 3)
x
x
2
2
2
2
5 2
( 3) ( 3)
3 2
( 3) ( 3)
5 4
( 3) ( 3)
2 5
( 3) ( 3)
x x
x x
x x
x x
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