Using partial fractions - why is it Ax+B/x^2 and not A/x + B/x^2?

Thread starter IntegrateMe
Start date Jan 19, 2010
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Fractions Partial Partial fractions

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The discussion centers on the decomposition of the rational function (-2x^2 + 10x + 8) / [x^2(x + 2)] into partial fractions. The correct form is identified as Ax + B/x^2 + C/x + 2, rather than A/x + Bx + C/x^2 + D/x + 2. The confusion arises from the treatment of the x^2 term, where splitting it leads to redundancy in the coefficients. The rationale for not splitting the x^2 term is to maintain a simpler and more efficient representation of the function. Understanding this helps clarify the structure of partial fraction decomposition in rational expressions.

Jan 19, 2010

IntegrateMe

Partial fractions of (-2x²+10x+8)/[x²(x+2)]

I initally thought that it was A/x + Bx+C/x² + D/x+2 but you really just do Ax+B/x² + C/x+2 ...can anyone explain why the "x²" isn't split?

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Jan 19, 2010

Dick

Science Advisor

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A/x+(B+Cx)/x^2=A/x+B/x^2+C*x/x^2=A/x+C/x+B/x^2. Doesn't that make the C term sort of redundant?

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