To find an expression equivalent to [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex], follow these steps:
1. Convert Division by a Fraction to Multiplication:
Recall that division by a fraction is equivalent to multiplication by its reciprocal. Hence,
[tex]\[
\frac{m-4}{m+4} \div (m+2) = \frac{m-4}{m+4} \times \frac{1}{m+2}
\][/tex]
2. Multiplication of Fractions:
When multiplying two fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{m-4}{m+4} \times \frac{1}{m+2} = \frac{(m-4) \times 1}{(m+4) \times (m+2)} = \frac{m-4}{(m+4)(m+2)}
\][/tex]
Therefore, the expression [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex] simplifies to [tex]\(\frac{m-4}{(m+4)(m+2)}\)[/tex].
Thus, the equivalent expression is:
[tex]\[
\boxed{\frac{m-4}{(m+4)(m+2)}}
\][/tex]
