Let's simplify the given expression step by step:

$\frac{x^2 - 2x}{(x-2)(x+3)}$

Step 1: Factor the Numerator

The numerator $x^2 - 2x$ can be factored as:

$x(x - 2)$

So the expression becomes:

$\frac{x(x - 2)}{(x - 2)(x + 3)}$

Step 2: Cancel Out Common Factors

Since $(x - 2)$ appears in both the numerator and denominator, we cancel it:

$\frac{x}{x + 3}$

Step 3: Identify the Correct Answer

The simplified expression is:

$\frac{x}{x + 3}$

From the given multiple-choice options, the correct answer is C.

Would you like a more detailed explanation or have any questions?

Here are five related questions you might find useful:

1. How do you factor quadratic expressions like $x^2 - 2x$?
2. What are the rules for canceling terms in a fraction?
3. How do restrictions on variables affect simplifications?
4. How can you simplify more complex rational expressions?
5. What happens if there are no common factors to cancel?

Tip: Always check for factors in both the numerator and denominator before canceling terms to avoid mistakes!