# Re: Partial fraction decomposition

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Posted by Ryan on September 30, 2002 at 08:08:27:

In Reply to: Partial fraction decomposition posted by sash on September 30, 2002 at 02:46:37:

multiply each term by the LCD (lowest commen Denominator) Then simplify by grouping all the terms with x^2 together, terms with X, x^3, Constants, etc. Fator out the X^4 , and the X, etc.. Then set systems of equations up. For example ( but not in your problem) You may have [A + B]X^2 then you know that A+B = the coefficient for the X^2 term in the original equation. IF you had [A+2C]X and there was no X term in the orig. You would have A=0 and C=0 or A=2 and C= -1. If you set up the systems - most are degenerate and wind up very simple.

EX: A/(x+1) + Bx+c/ (x^2-4) = (x^2 + 4)/ [(x+1)(x^2-4)]

A(x^2-4) + (bx+C)(X+1) = (X^2 +4)
AX^2 -4A + BX^2+C+BX+CX = (x^2 + 4)

[A+B]X^2 + [ B+C]X + [-4A+c]
solve: a+b=1 , B+c = 0, -4a+c=4
Then just substitute back in and integrate.

: A/(x-1)+ B/(x-10^2+ C/(x-1)^3+ D/(x+7)+ Ex+F/(x^2+4)+Gx+H/(x^2+4).

: this is the denominator of a long partial fraction which I've factorised the denominator,But i can't solve for the uknown variables please show me how, if you can with the full process.

: Thank you

: Sash.

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