Question

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

Explanation:

Step1: Recall division of fractions rule

To divide by a number, we multiply by its reciprocal. So, \(\frac{a}{b}\div c=\frac{a}{b}\times\frac{1}{c}\) (where \(c
eq0\) and \(b
eq0\)).

Here, \(a = m - 4\), \(b=m + 4\), and \(c=m + 2\). So, \(\frac{m - 4}{m + 4}\div(m + 2)=\frac{m - 4}{m + 4}\times\frac{1}{m + 2}\)

Step2: Multiply the fractions

When multiplying fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\) (where \(b
eq0\) and \(d
eq0\)).

Applying this, \(\frac{m - 4}{m + 4}\times\frac{1}{m + 2}=\frac{(m - 4)\times1}{(m + 4)\times(m + 2)}=\frac{m - 4}{(m + 4)(m + 2)}\)

Answer:

A. \(\frac{m - 4}{(m + 4)(m + 2)}\)