1. **State the problem:** Find the domain of the rational expression $$\frac{4-x}{3x+21}$$. 2. **Recall the domain rule for rational expressions:** The denominator cannot be zero because division by zero is undefined. 3. **Set the denominator equal to zero and solve:** $$3x + 21 = 0$$ 4. **Solve for $x$:** $$3x = -21$$ $$x = \frac{-21}{3}$$ $$x = -7$$ 5. **Interpretation:** The expression is undefined at $x = -7$, so the domain is all real numbers except $-7$. **Final answer:** The domain is all real numbers except $-7$.