Solving for Coefficients in Partial Fractions Example


© 2001 by Karl Hahn 		KCT logo

Here is the procedure for solving the linear equations in the example for A, B, and C by the method of Gaussian elimination. Each procedure tells you how to get from the current set of equations to the next set of equations.

EquationsProcedure

     A  +    B  +    C  =    1

   -5A  -   2B  -    C  =    4

    6A  -   3B  -   2C  =  -33
Add 5 times first equation to second equation. Subtract 6 times first equation from third equation. 



     A  +    B  +    C  =    1

            3B  +   4C  =    9

           -9B  -   8C  =  -39
Add 3 times second equation to third equation. 



     A  +    B  +    C  =    1

            3B  +   4C  =    9

                    4C  =  -12
Subtract third equation from second equation. 



     A  +    B  +    C  =    1

            3B          =   21

                    4C  =  -12
Subtract one third of second equation from first equation. 



     A  +            C  =   -6

            3B          =   21

                    4C  =  -12
Subtract one quarter of third equation from first equation. 



     A                  =   -3

            3B          =   21

                    4C  =  -12
Divide constants out of second and third equations to get solution. 



     A                  =   -3

             B          =    7

                     C  =   -3
Done.

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