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Factors in Denominator and Partial Fraction Decomposition
Factor in denominator
Term in partial fraction decomposition
ax + b
A
( ax + b )k
A1 + A2 + L + Ak , k = 1, 2, 3,K
ax + b ( ax + b )2 ( ax + b )k
ax2 + bx + c
Ax + B
(ax2 + bx + c )k
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
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.
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