Answer:
[tex] \frac{1}{(m - 4)(m + 3)} [/tex]
Step-by-step explanation:
We want to find an expression that is equivalent to
[tex] \frac{m + 3}{ {m}^{2} - 16} \div \frac{ {m}^{2} - 9 }{m + 4} [/tex]
First, multiply by the reciprocal of the second fraction.
[tex]\frac{m + 3}{ {m}^{2} - 16} \times \frac{m + 4}{ {m}^{2} - 9 } [/tex]
We now factor to obtain:
[tex]\frac{m + 3}{ (m + 4)(m - 4)} \times \frac{m + 4}{(m + 3)(m - 3)} [/tex]
We cancel common factors to get:
[tex]\frac{1}{ m - 4} \times \frac{1}{m - 3} = \frac{1}{(m - 4)(m + 3)} [/tex]
