116. (\(\frac{1}{m - n} - \frac{1}{m + n}\)) : \(\frac{2}{3m - 3n}\).

116. Упростим выражение:

\((\frac{1}{m - n} - \frac{1}{m + n}\)) : \(\frac{2}{3m - 3n}\) = \(\frac{(m + n) - (m - n)}{(m - n)(m + n)} : \frac{2}{3(m - n)}\) = \(\frac{m + n - m + n}{m^2 - n^2} : \frac{2}{3(m - n)}\) = \(\frac{2n}{m^2 - n^2} \cdot \frac{3(m - n)}{2}\) = \(\frac{2n \cdot 3(m - n)}{(m - n)(m + n) \cdot 2}\) = \(\frac{6n(m - n)}{2(m - n)(m + n)}\) = \(\frac{3n}{m + n}\)

Ответ: \(\frac{3n}{m + n}\)