To determine which expression is equivalent to [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex], we need to simplify the given expression step-by-step:
1. Start with the given expression:
[tex]\[
\frac{m-4}{m+4} \div (m+2)
\][/tex]
2. Recall that dividing by a number is the same as multiplying by its reciprocal. Using this property, we can rewrite the division as multiplication with the reciprocal of [tex]\(m+2\)[/tex]:
[tex]\[
\frac{m-4}{m+4} \div (m+2) = \frac{m-4}{m+4} \times \frac{1}{m+2}
\][/tex]
3. Combine the fractions using the multiplication rule for fractions (multiply the numerators together and the denominators together):
[tex]\[
\frac{m-4}{m+4} \times \frac{1}{m+2} = \frac{m-4}{(m+4)(m+2)}
\][/tex]
4. Therefore, the simplified expression is:
[tex]\[
\frac{m-4}{(m+4)(m+2)}
\][/tex]
By following these steps, we find that the expression equivalent to [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex] is:
[tex]\[
\boxed{\frac{m-4}{(m+4)(m+2)}}
\][/tex]
