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Index
Programmed tutorial: Partial Fractions Example 1
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Find the
partial fraction decomposition
of
General Contents
Detailed Contents
Index
What do we do first?
Factor the denominator.
Do that.
Set up the partial fractions.
How do we proceed?
We can determine A and B by combining the fractions on the right hand side.
What is the least common denominator for them?
(
x
– 4)*(
x
+ 3)
Combine the fractions.
We know that this can be satisfied by all values of x, and that the numerators must be equal.
In particular, we can use convenient values of x: –3 and +4.
Try
x
= –3.
Then, equating the numerators in equation 1, we get
Simplify.
Solve.
B
= 3
Now try
x
=
4
in equation 1.
We get
Simplify.
Solve.
Now substitute these values into the original fraction,
F
, in equation 1 as its partial fraction expansion.
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