Determine the partial fraction decomposition of `(8x^2-12)/(x(x^2+2x-6))`

Explanation

To determine the partial fraction decomposition of the expression \(\frac{8x^2 - 12}{x(x^2 + 2x - 6)}\), we will follow these steps:

### Step 1: Set Up the Partial Fraction Decomposition
We can express the given fraction as a sum of simpler fractions. Since the denominator consists of a linear factor \(x\) and a quadratic factor \(x^2 + 2x - 6\), we can write:
\[ \frac{8x^2 - 12}{x(x^2 + 2x - 6)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 2x - 6} \]
where \(A\), \(B\), and \(C\) are constants that we need to determine.
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