$$\frac{ m+n }{ m } \times \frac{ mn }{ 3m+3n }$$
$\frac{n}{3}$
$$\frac{\left(m+n\right)mn}{m\left(3m+3n\right)}$$
$$\frac{n\left(m+n\right)}{3m+3n}$$
$$\frac{n\left(m+n\right)}{3\left(m+n\right)}$$
$$\frac{n}{3}$$
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