Divide. Write the answer in lowest terms. \( \frac{9}{x-4} \div \frac{63}{3 x-12} \) \( \frac{9}{x-4} \div \frac{63}{3 x-12}=\square \) (Simplify your answer.)

1. Rewrite the division as multiplication by the reciprocal: \[ \frac{9}{x-4} \div \frac{63}{3x-12} = \frac{9}{x-4} \times \frac{3x-12}{63} \] 2. Factor the numerator \(3x-12\): \[ 3x-12 = 3(x-4) \] So, the expression becomes: \[ \frac{9}{x-4} \times \frac{3(x-4)}{63} \] 3. Cancel the common factor \((x-4)\) (with the condition \(x \neq 4\)): \[ = \frac{9}{\cancel{x-4}} \times \frac{3\,\cancel{(x-4)}}{63} \] 4. Multiply the remaining terms: \[ = \frac{9 \times 3}{63} = \frac{27}{63} \] 5. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, 9: \[ \frac{27 \div 9}{63 \div 9} = \frac{3}{7} \] Thus, the simplified result is: \[ \frac{9}{x-4} \div \frac{63}{3x-12} = \frac{3}{7} \]