Question: \[\frac{x-4}{(x-4)(\sqrt{x+2})}\]
1. **State the problem:** Simplify the expression $$\frac{x-4}{(x-4)(\sqrt{x+2})}$$.
2. **Identify the formula and rules:** When simplifying fractions, if the numerator and denominator share a common factor, we can cancel that factor, provided it is not zero.
3. **Simplify the expression:**
$$\frac{x-4}{(x-4)(\sqrt{x+2})} = \frac{\cancel{x-4}}{\cancel{x-4} \cdot \sqrt{x+2}}$$
4. **After canceling the common factor:**
$$= \frac{1}{\sqrt{x+2}}$$
5. **Important note:** The simplification is valid only if $$x-4 \neq 0$$, i.e., $$x \neq 4$$, because division by zero is undefined.
**Final answer:**
$$\frac{1}{\sqrt{x+2}} \quad \text{for} \quad x \neq 4$$