Factors in Denominator and Partial Fraction Decomposition
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Factor in denominator
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Term in partial fraction decomposition
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ax + b
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A
ax + b
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( ax + b )k
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A1 + A2 + L + Ak , k = 1, 2, 3,K
ax + b ( ax + b )2 ( ax + b )k
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ax2 + bx + c
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Ax + B
ax2 + bx + c
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(ax2 + bx + c )k
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A1 x + B1 + A2 x + B2 + L + Ak x + Bk , k = 1, 2, 3,K
ax2 + bx + c (ax2 + bx + c )2 (ax2 + bx + c )k
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Note: that the first and third cases are really special cases of the second and fourth cases correspondingly.
There are various methods for determining the coefficients for every term and we will go over each of those in the example.