Decomposition of
N(x) / D(x) into Partial Fractions
1. Divide if improper: If N(x)/D(x) is
an improper fraction ( that is, id the degree of the
numerator is greater than or equal to the degree of the
denominator), divide the denominator into the numerator to
obtain
N(x)/D(x) = ( a polynomial) + N1(x)/D(x)
2. Factor Denominator: Completely factor the
denominator into factors of the form
( px + q )m
and ( ax2 + bx + c
)n
where ax2 + bx + c is irreducible.
3. Linear factors: For each factor of
the form ( px + q )m , the partial fraction
decomposition must include the following sum of m
fractions.
(A1/( px + q )) + (A2/(
px + q )2) + ... .+ (Am/(
px + q )m)
4. Quadratic factors: For each factor of the
form ( ax2 + bx + c )n,
the partial fraction decomposition must include the
following sum of n fractions.
((B1x + C1)/( ax2
+ bx + c )) + ((B2x
+ C2)/(ax2 + bx
+ c )2) + ... .+ ((Bnx
+ Cn)/( ax2 + bx
+ c )n)
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