Let's simplify the given expression step-by-step to determine which option is equivalent to [tex]\(\frac{m-4}{m+4} \div(m+2)\)[/tex].
### Step 1: Rewrite the Division as Multiplication by the Reciprocal
The expression [tex]\(\frac{m-4}{m+4} \div(m+2)\)[/tex] can be rewritten using the property of division as multiplication by the reciprocal:
[tex]\[
\frac{m-4}{m+4} \div (m+2) = \frac{m-4}{m+4} \times \frac{1}{m+2}
\][/tex]
### Step 2: Multiply the Expressions
Next, we multiply the two fractions:
[tex]\[
\frac{m-4}{m+4} \times \frac{1}{m+2} = \frac{m-4}{(m+4)(m+2)}
\][/tex]
### Step 3: Simplify the Expression
Since there are no common factors in the numerator and the denominator that we can cancel out, the expression remains as:
[tex]\[
\frac{m-4}{(m+4)(m+2)}
\][/tex]
### Conclusion
Thus, the equivalent expression to [tex]\(\frac{m-4}{m+4} \div(m+2)\)[/tex] is:
[tex]\[
\frac{m-4}{(m+4)(m+2)}
\][/tex]
So, the correct answer is:
[tex]\[
\frac{m-4}{(m+4)(m+2)}
\][/tex]
