1. **State the problem:** Simplify the expression $\frac{x - 3}{x(x + 2)}$. 2. **Understand the expression:** The numerator is $x - 3$ and the denominator is $x(x + 2)$. 3. **Check for common factors:** There are no common factors between numerator and denominator since $x - 3$ cannot be factored further to include $x$ or $x + 2$. 4. **Final simplified form:** The expression remains as $$\frac{x - 3}{x(x + 2)}$$ This is the simplest form since numerator and denominator share no common factors. **Answer:** $$\frac{x - 3}{x(x + 2)}$$