The denominator in the given expression is \((x+2)(x+1)^2\). Since \(x+2\) is a linear factor and \((x+1)^2\) is a repeated linear factor, the partial fraction decomposition will have the form:
\[
\frac{x-3}{(x+2)(x+1)^2} = \frac{A}{x+2} + \frac{B}{x+1} +
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