Determine the partial fraction decomposition of `(3x^3+7x-4)/((x^2+2)^2)`

Explanation

To determine the partial fraction decomposition of the expression \(\frac{3x^3 + 7x - 4}{(x^2 + 2)^2}\), we will follow these steps:

### Step 1: Set up the partial fraction decomposition
Since the denominator \((x^2 + 2)^2\) is a repeated irreducible quadratic factor, we can express the decomposition as:
\[ \frac{3x^3 + 7x - 4}{(x^2 + 2)^2} = \frac{Ax + B}{x^2 + 2} + \frac{Cx + D}{(x^2 + 2)^2} \]

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