12 (n+8)/(5n(n+8))div (3n)/(3n(n-2))

To simplify the given expression, we can follow these steps:<br /><br />1. Rewrite the division as multiplication by the reciprocal:<br /> $12 \frac {n+8}{5n(n+8)} \div \frac {3n}{3n(n-2)} = 12 \frac {n+8}{5n(n+8)} \times \frac {3n(n-2)}{3n}$<br /><br />2. Cancel out common factors in the numerator and denominator:<br /> $12 \frac {n+8}{5n(n+8)} \times \frac {3n(n-2)}{3n} = 12 \frac {n+8}{5n} \times \frac {3n-6}{3n}$<br /><br />3. Simplify the expression:<br /> $12 \frac {n+8}{5n} \times \frac {3n-6}{3n} = 12 \frac {3n-6}{15n} = 12 \frac {n-2}{5n}$<br /><br />Therefore, the simplified expression is $12 \frac {n-2}{5n}$.