Determine the partial fraction decomposition of `(8x-42)/(x^2+3x-18)`

Explanation

To determine the partial fraction decomposition of the expression \(\frac{8x - 42}{x^2 + 3x - 18}\), we will follow these steps:

### Step 1: Factor the Denominator
First, we need to factor the quadratic expression in the denominator, \(x^2 + 3x - 18\).

To factor it, we look for two numbers that multiply to \(-18\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers \(6\) and \(-3\) satisfy this condition.

Thus, we can factor the denominator as:
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