What is the quotient? \( \frac{n+3}{2 n-6} \div \frac{n+3}{3 n-9} \)

To find the quotient, we first rewrite the division of fractions as multiplication by the reciprocal. Thus, we have: \[ \frac{n+3}{2n-6} \div \frac{n+3}{3n-9} = \frac{n+3}{2n-6} \times \frac{3n-9}{n+3} \] Next, we can simplify this expression. Notice that \(n+3\) in the numerator of the second fraction will cancel with \(n+3\) in the first fraction: \[ = \frac{1}{2n-6} \times (3n-9) \] Now we can simplify \(3n-9\) as \(3(n-3)\) and \(2n-6\) as \(2(n-3)\). This gives us: \[ = \frac{3(n-3)}{2(n-3)} \] We can once again cancel \(n-3\) (assuming \(n \neq 3\)): \[ = \frac{3}{2} \] Thus, the final quotient is: \[ \frac{3}{2} \]