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Express rational functions as a sum of fractions with simpler denominators. You can apply this to telescoping series to mass cancel terms in a seemingly complicated sum.

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Suppose \(a\), \(b\), and \(c\) are constants such that the following holds for all real numbers \(x\) such that all of the denominators are nonzero:

\[\frac{9}{x(x+1)^2}=\frac{a}{x}+\frac{b}{x+1}+\frac{c}{(x+1)^2}.\] What is the value of \(abc?\)

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