Simplofy \( \frac{4}{n-3} \div \frac{8 a}{3 n-9}= \)

To simplify the expression \( \frac{4}{n-3} \div \frac{8 a}{3 n-9} \), we first rewrite the division as multiplication by the reciprocal: \[ \frac{4}{n-3} \times \frac{3n-9}{8a} \] Next, we can factor \( 3n-9 \) as \( 3(n-3) \): \[ \frac{4}{n-3} \times \frac{3(n-3)}{8a} \] Now, we can cancel the \( n-3 \) in the numerator and denominator: \[ \frac{4 \times 3}{8a} = \frac{12}{8a} \] Finally, we simplify \( \frac{12}{8} \) to \( \frac{3}{2} \): \[ \frac{3}{2a} \] So, the simplified expression is: \[ \frac{3}{2a} \]