Step-by-step explanation:
[tex] \frac{m + 3}{ {m}^{2} - 16} \div \frac{ {m}^{2} - 9 }{m + 4} \\ \\ = \frac{m + 3}{ {m}^{2} - {4}^{2} } \div \frac{ {m}^{2} - {3}^{2} }{m + 4} \\ \\ = \frac{m + 3}{ ({m} + 4)(m - {4})} \div \frac{ ({m} + 3)(m- {3}) }{m + 4} \\ \\ = \frac{m + 3}{ ({m} + 4)(m - {4})} \times \frac{ m + 4 }{({m} + 3)(m- {3})} \\ \\ = \frac{1}{ (m - {4})} \times \frac{ 1}{(m- {3})} \\ \\ = \frac{1 \times 1}{ (m - {4}) \times (m- {3})} \\ \\ = \frac{1}{ m^{2} + ( - 4 - 3)m + ( - 4)( - 3)} \\ \\ = \frac{1}{ m^{2} + ( - 7)m + 12} \\ \\ = \frac{1}{ m^{2} - 7m + 12} [/tex]
