Find the coefficient of `x^(n)` in the expansion of `(x)/((x-3)(x-2))` in powers of x specifying the interval in which the expansion is valid.

Answer

To find the coefficient of \( x^n \) in the expansion of \( \frac{x}{(x-3)(x-2)} \), we will follow these steps:

### Step 1: Partial Fraction Decomposition
We start with the expression:
\[ \frac{x}{(x-3)(x-2)} \]
We can express this as:
\[ \frac{x}{(x-3)(x-2)} = \frac{A}{x-2} + \frac{B}{x-3} \]
where \( A \) and \( B \) are constants that we need to determine.