Find the domain of the expression. $$ \begin{array}{l}\frac{\sqrt{x-4}}{x+6} \ x \neq 4 \ x \neq-6 \ \text { all real numbers } \ x \geq 4\end{array} $$

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To determine the domain of the expression:

$$
\frac{\sqrt{x - 4}}{x + 6}
$$

we need to consider two main conditions:

1. **Square Root Requirement**:
   - The expression inside the square root must be non-negative.
   $$
   x - 4 \geq 0 \implies x \geq 4
   $$

2. **Denominator Restriction**:
   - The denominator cannot be zero.
   $$
   x + 6 \neq 0 \implies x \neq -6
   $$

However, when considering $$ x \geq 4 $$, the value $$ x = -6 $$ is already excluded since $$-6 < 4$$. Therefore, the only necessary condition to define the domain is:

$$
x \geq 4
$$

**Conclusion**:
The domain of the expression is all real numbers $$ x $$ such that $$ x \geq 4 $$.

**Answer**: $$ x \geq 4 $$
The domain of the expression is all real numbers $$ x $$ where $$ x \geq 4 $$.

Find the domain of the expression. \[ \begin{array}{l}\frac{\sqrt{x-4}}{x+6} \\ x \neq 4 \\ x \neq-6 \\ \text { all real numbers } \\ x \geq 4\end{array} \]

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