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Partial Fractions
P
ARTIAL
F
RACTION
D
ECOMPOSITION
Given a rational expression, we will find simpler rational expressions whose sum is the given expression.
Examples.
5
6
=
1
2
+
1
3
5
x
 6
x
(
x
+ 3)
=
2
x
+
7
x
+ 3
Partial Fraction Decomposition Theorem
If
f
(
x
) =
p
(
x
)
q
(
x
)
is a rational expression in which the degree of the numerator is less than the degree of the
denominator, and
p
(
x
) and
q
(
x
) have no common factors, then
f
(
x
) can be decomposed in the
form
f
(
x
) =
f
1
(
x
) +
f
2
(
x
) + . . . +
f
n
(
x
)
where each
f
i
(
x
) has one of the following forms:
A
(
ax
+
b
)
m
or
Bx
+
C
(
ax
2
+ bx
+
c
)
m
NOTE: The procedure for partial fraction decomposition depends on the factorization of the
denominator.
F
OUR
P
OSSIBLE
C
ASES:
Case 1
Nonrepeated Linear Factors
The partial fraction decomposition will contain an expression of the form
A
x
+
a
for each nonrepeated
linear factor of the denominator.
Example.
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This note was uploaded on 04/13/2008 for the course MATH 2412 taught by Professor Matroy during the Spring '08 term at Alamo Colleges.
 Spring '08
 MatRoy
 Rational Expressions, Fractions

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