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Determine the partial fraction decomposi...

Determine the partial fraction decomposition of `(x^2+3x-15)/((x^2+9)(x^2+x+1))`

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To determine the partial fraction decomposition of the expression \(\frac{x^2 + 3x - 15}{(x^2 + 9)(x^2 + x + 1)}\), we will follow these steps: ### Step 1: Set up the partial fractions We start by expressing the fraction as a sum of partial fractions. Since the denominator consists of two quadratic factors, we can write: \[ \frac{x^2 + 3x - 15}{(x^2 + 9)(x^2 + x + 1)} = \frac{Ax + B}{x^2 + 9} + \frac{Cx + D}{x^2 + x + 1} \] ...
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