Unformatted text preview: peaking of which, let’s get started on some examples. Example 1 Determine the partial fraction decomposition of each of the following.
8 x  42
(a) 2
[Solution]
x + 3 x  18
9  9x
(b)
[Solution]
2
2x + 7 x  4
4x2
(c) (d) ( x  1)( x  2 )
9 x + 25 ( x + 3) 2 2 [Solution] [Solution] Solution
We’ll go through the first one in great detail to show the complete partial fraction process and
then we’ll leave most of the explanation out of the remaining parts.
(a) 8 x  42
x + 3x  18
2 The first thing to do is factor the denominator as much as we can. 8 x  42
8 x  42
=
x + 3 x  18 ( x + 6 )( x  3)
2 So, by comparing to the table above it looks like the partial fraction decomposition must look
like, A
B
8 x  42
=
+
x + 3x  18 x + 6 x  3
2 Note that we’ve got different coefficients for each term since there is no reason to think that they
will be the same.
Now, we need to determine the values of A and B. The first step is to actually add the two terms
back up. This is usually simpler than it might appear to be. Recall that we first need the least
common denominator, but we’ve already got that from th...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
 Spring '12
 MrVinh

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