Which expression is equivalent to the expression below? \( \frac{\frac{m+3}{m^{2}-16}}{\frac{m^{2}-9}{m+4}} \)

To simplify the expression \( \frac{\frac{m+3}{m^{2}-16}}{\frac{m^{2}-9}{m+4}} \), we can multiply by the reciprocal of the denominator: 1. Rewrite it as \( \frac{m+3}{m^{2}-16} \times \frac{m+4}{m^{2}-9} \). 2. Now factor \( m^2 - 16 \) and \( m^2 - 9 \): - \( m^2 - 16 = (m - 4)(m + 4) \) - \( m^2 - 9 = (m - 3)(m + 3) \) Now substitute the factored forms into the expression: \[ \frac{m+3}{(m-4)(m+4)} \times \frac{m+4}{(m-3)(m+3)} \] Now, we can cancel out \( m+3 \) and \( m+4 \) (assuming \( m \neq -3 \) and \( m \neq -4 \) to avoid division by zero): \[ \frac{1}{m - 4} \times \frac{1}{m - 3} = \frac{1}{(m - 4)(m - 3)} \] So, the expression simplifies to: \[ \frac{1}{(m - 4)(m - 3)} \] Thus, the equivalent expression is \( \frac{1}{(m - 4)(m - 3)} \).