General Contents
Detailed Contents
Index
Programmed tutorial: Partial Fractions Example 5
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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
+ 7)
Combine the fractions.
Do the multiplication.
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
Substitution and Elimination Methods
will help us get to two equations in 2 unknowns.
Solve the first equation for
B
.
B
= –
A
Use this to rewrite equation 2 in terms of
A
and
C
.
We get 3
A
+
C
=
10
Equation 4
Which equation might we combine with this one?
Since equation 4 involves only
A
and
C
, we should attempt to combine it with equation 3.
Can we just add the equations?
No.
First we need to multiply equation 4 by the constant 3 so that the “
C
” terms will eliminate.
Now combine (three times equation 4) and equation 3.
We get
Adding, we get
, or
A
= 2
Use this in equation 3 to find
C
.
, or
C
= 4
Use the result for
A
in equation 1 to find
B
.
B
= -2
Finally, use these results to rewrite
F
(
s
) in partial fractions.
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