Question

which expression is equivalent to \\(\frac{m - 4}{m + 4} \div (m + 2)\\)? \\(\frac{(m + 4)(m + 2)}{m - 4}\\) \\(\frac{m - 4}{(m + 4)(m + 2)}\\) \\(\frac{m + 4}{(m - 4)(m + 2)}\\) \\(\frac{(m - 4)(m + 2)}{m + 4}\\)

Explanation:

Step1: Recall division of fractions rule

To divide by a number, multiply by its reciprocal. So, \(\frac{m - 4}{m + 4}\div(m + 2)=\frac{m - 4}{m + 4}\times\frac{1}{m + 2}\)

Step2: Multiply the fractions

Multiply the numerators and denominators: \(\frac{(m - 4)\times1}{(m + 4)\times(m + 2)}=\frac{m - 4}{(m + 4)(m + 2)}\)

Answer:

\(\frac{m - 4}{(m + 4)(m + 2)}\) (the second option among the given ones)