To solve the expression

\[
C = \frac{x + 2}{x + 3} + \frac{2x - 1}{x - 2} - \frac{13x}{x^2 - 9}
\]

we first note that \(x^2 - 9\) can be factored as \((x - 3)(x + 3)\).

Next, we determine a common denominator for the three fractions involved. The common denominator will be

\[
(x + 3)(x - 2)(x - 3)
\]

Now, we rewrite each term with this common denominator:

1. For \(\frac{x + 2}{x + 3}\), we multiply the numerator and denominator by \((x - 2)(x - 3)\):
\[
\frac{(x + 2)(x - 2)(x - 3)}{(x + 3)(x - 2)(x - 3)}
\]

2. For \(\frac{2x - 1}{x - 2}\), we multiply by \((x + 3)(x - 3)\):
\[
\frac{(2x - 1)(x + 3)(x - 3)}{(x - 2)(x + 3)(x - 3)}
\]

3. For \(-\frac{13x}{x^2 - 9}\), we treat it as \(-\frac{13x}{(x + 3)(x - 3)}\), and multiply by \((x - 2)\):
\[
-\frac{13x(x - 2)}{(x + 3)(x - 3)(x - 2)}
\]

Now we can combine all three fractions:
\[
C = \frac{(x + 2)(x - 2)(x - 3) + (2x - 1)(x + 3)(x - 3) - 13x(x - 2)}{(x + 3)(x - 2)(x - 3)}
\]

Next, we simplify the numerator step-by-step. First, expand each term:
1. Expand \((x + 2)(x - 2)(x - 3)\).
2. Expand \((2x - 1)(x + 3)(x - 3)\).
3. Expand \( -13x(x - 2)\).

After expanding, combine like terms in the numerator. This may lead to a polynomial that could also be factored further if suitable.

Finally, the resulting form of \(C\) will be a rational function where the numerator and denominator are polynomials. To simplify, check for cancelation of common factors between the numerator and the denominator.

This process may involve multiple steps of calculation; ensure you check each stage for simplifications. If you want specific numerical examples or further assumptions (like particular values for \(x\)), please provide that!