Factors in denominator and partial fraction decomposition, Mathematics

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Factors in Denominator and Partial Fraction Decomposition

Factor in denominator

Term in partial  fraction decomposition

 

ax + b

A

ax + b

 

( 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

 

(ax2  + bx + c )k

Ax 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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