General Contents
Detailed Contents
Index
Programmed tutorial: Partial Fractions Example 4
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Find the
partial fraction decomposition
of
General Contents
Detailed Contents
Index
Set up the partial fractions.
How do we proceed?
We can determine
A
,
B
, and
C
by combining the terms on the right hand side.
What is the least common denominator for them?
(
s
– 3) * (
s
+ 2) * (
s
+ 4)
Combine the fractions?
Distribute the multiplication on the right-hand side.
Collect like terms.
What do we do next?
We equate coefficients of like powers of
s
.
Do that.
Using the numerators of the last equation, we get
Equation 1
Equation 2
Equation 3
We have 3 equations in the 3 unknowns:
A, B,
and
C
. How can we solve for them?
The
Elimination Method
will help us get to two equations in 2 unknowns.
Add equations 1 and 2 to eliminate
C.
We get
Equation 4
Add 6 times equation 1 to equation 3 to get another equation involving
A
and
B
.
We get
Equation 5
Now combine (–2) times equation 4 and equation 5.
We get
Adding, we get
, or
B
= 1
Use this in equation 4 to find
A
.
, or
A
= 5
Use these results for
A
and
B
in equation 1 to find
C
.
, or
C
= –6
Use these results to rewrite
F
(
s
) in terms of partial fractions.
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