Use Gaussian Elimination to solve for A, B, C of the Partial Fraction Decomposition Equation.

(x+3)/(x^2(x-1)) = A/x+B/x^2+C/(x-1)

I have expanded it by multiplying by the LCD but do not know how to equate coefficients or set up equations to use Gaussian Elimination..

x+3 = A (x^2-x) +B(x-1) +Cx^2

Any help please :)))

Question

Use Gaussian Elimination to solve for A, B, C of the Partial Fraction Decomposition Equation. 

(x+3)/(x^2(x-1)) = A/x+B/x^2+C/(x-1)

I have expanded it by multiplying by the LCD but do not know how to equate coefficients or set up equations to use Gaussian Elimination..

x+3 = A (x^2-x) +B(x-1) +Cx^2

Any help please :)))

hero · Answer

Use this to help: http://calc101.com/webMathematica/partial-fractions.jsp#topdoit

anonymous · Answer

$$x+3=A \left( x ^{2}-x \right)+B \left( x-1 \right)+C x ^{2}=\left( A+C \right)x ^{2}+\left( -A-B \right)x-B$$
now equating co-efficients
0=A+C
1=-A-B
3=-B
now you can find the values of A and C

anonymous · Answer

I tried using the Calc 101 website but kept getting the syntax wrong. But I will try it in the future

anonymous · Answer

@surjithayer: I found the values for A and C using your method. But how do I use Gaussian elimination from there?

anonymous · Answer

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