Представьте в виде дроби выражение: (m^2+n^2)/(3m+3n) :(2m/(m+n)+(m-n)/m).

Ответ:

\[\frac{m^{2} + n^{2}}{3m + 3n}\ \ :\left( \frac{2m^{\backslash m}}{m + n} + \frac{n - m^{\backslash m + n}}{m} \right) =\]

\[= \frac{m^{2} + n^{2}}{3m + 3n}\ :\frac{2m^{2} + n^{2} - m^{2}}{m(m + n)} =\]

\[= \frac{m^{2} + n^{2}}{3m + 3n}\ :\frac{m^{2} + n^{2}}{m(m + n)} =\]

\[= \frac{\left( m^{2} + n^{2} \right) \cdot m \cdot (m + n)}{3(m + n)(m^{2} + n^{2})} = \frac{m}{3}.\]