Simplify DONE \( \frac{\frac{16 m^{2}}{m^{2}+5}}{3 m^{2}+15} \) DOS

1. Start with the given expression: \[ \frac{\frac{16 m^{2}}{m^{2}+5}}{3 m^{2}+15} \] 2. Interpret the division as multiplication by the reciprocal: \[ \frac{16 m^{2}}{m^{2}+5} \cdot \frac{1}{3 m^{2}+15} \] 3. Factor the denominator \(3 m^{2}+15\): \[ 3 m^{2}+15 = 3(m^{2}+5) \] Hence, the expression becomes: \[ \frac{16 m^{2}}{m^{2}+5} \cdot \frac{1}{3(m^{2}+5)} \] 4. Multiply the numerators and denominators: \[ \frac{16 m^{2}}{3(m^{2}+5)(m^{2}+5)} = \frac{16 m^{2}}{3 (m^{2}+5)^2} \] 5. The simplified expression is: \[ \frac{16 m^{2}}{3 (m^{2}+5)^2} \]