Solving for Coefficients in Partial Fractions Example © 2001 by Karl Hahn

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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.

Equations		Procedure
A + B = 1 -2A + 3B + C = -3 A + 3C = 46		Add 2 times first equation to second equation. Subtract 17 times first equation from third equation.
A + B = 1 5B + C = -1 -17B + 3C = 29		Multiply third equation by 5
A + B = 1 5B + C = -1 -85B + 15C = 145		Add 17 times second equation to third equation.
A + B = 1 5B + C = -1 32C = 128		Divide 32 out of third equation
A + B = 1 5B + C = -1 C = 4		Subtract third equation from second equation.
A + B = 1 5B = -5 C = 4		Divide 5 out of second equation and subtract the result from the first equation
A = 2 B = -1 C = 4		Done.

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