Simplify. a) \( \frac{4}{n-3} \div \frac{89}{3 n-9}= \)

To simplify the expression \( \frac{4}{n-3} \div \frac{89}{3n-9} \), we first recognize that \( 3n-9 \) can be factored as \( 3(n-3) \). So the division can be rewritten as: \[ \frac{4}{n-3} \div \frac{89}{3(n-3)} = \frac{4}{n-3} \times \frac{3(n-3)}{89} \] Now, we can cancel \( n-3 \) from the numerator and the denominator: \[ = \frac{4 \times 3}{89} = \frac{12}{89} \] Thus, the final simplified expression is: \[ \frac{12}{89} \]