Determine the partial fraction decomposition of `(4x^2)/((x-1)(x-2)^2)`

Explanation

To determine the partial fraction decomposition of the expression \(\frac{4x^2}{(x-1)(x-2)^2}\), we will follow these steps:

### Step 1: Set up the partial fraction decomposition
We can express \(\frac{4x^2}{(x-1)(x-2)^2}\) as a sum of partial fractions:
\[ \frac{4x^2}{(x-1)(x-2)^2} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{(x-2)^2} \]
where \(A\), \(B\), and \(C\) are constants that we need to determine.
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