6) (5/(m-n) - 4/(m+n)) * (m+9n)/(m+n);

6) $$\left(\frac{5}{m-n} - \frac{4}{m+n}\right) \cdot \frac{m+9n}{m+n} = \left(\frac{5(m+n) - 4(m-n)}{(m-n)(m+n)}\right) \cdot \frac{m+9n}{m+n} = \frac{5m + 5n - 4m + 4n}{(m-n)(m+n)} \cdot \frac{m+9n}{m+n} = \frac{m+9n}{(m-n)(m+n)} \cdot \frac{m+9n}{m+n} = \frac{(m+9n)^2}{(m-n)(m+n)^2}$$

Ответ: $$\frac{(m+9n)^2}{(m-n)(m+n)^2}$$