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Review of Partial Fractions
The purpose of the method of partial fractions is to express a fraction having a complicated
polynomial denominator as the sum of fractions whose denominators are simpler polynomials.
Step 0
. Make sure that the degree of the numerator is strictly less than the degree of the
denominator.
If the degree of the numerator is equal or greater, use long division before using
partial fractions.
Step 1
.
Choose the form of the partial fraction decomposition.
(a)
Factor the denominator into linear and irreducible (nonfactorable) quadratic factors.
(b) Each repeated factor in the denominator requires multiple fractions in the decomposition.
For example, the expression
in the denominator requires three fractions — one with
ÐB "Ñ
$
denominator
, one with denominator
, and one with denominator
.
ÐB"Ñ
B"
$
2
(c) Each denominator which is a linear polynomial or a power of a linear polynomial requires
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 Fall '08
 Hastings

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