Реши примеры с действиями.

Конечно, сейчас решим эти примеры. 6) $\left(\frac{5}{m-n} - \frac{4}{m+n}\right) : \frac{m+9n}{m+n} = \frac{5(m+n) - 4(m-n)}{(m-n)(m+n)} : \frac{m+9n}{m+n} = \frac{5m+5n - 4m+4n}{(m-n)(m+n)} : \frac{m+9n}{m+n} = \frac{m+9n}{(m-n)(m+n)} \cdot \frac{m+n}{m+9n} = \frac{1}{m-n}$ 7) $\frac{x-2}{x+2} \cdot \left(x - \frac{x^2}{x-2}\right) = \frac{x-2}{x+2} \cdot \frac{x(x-2) - x^2}{x-2} = \frac{x-2}{x+2} \cdot \frac{x^2-2x - x^2}{x-2} = \frac{x-2}{x+2} \cdot \frac{-2x}{x-2} = \frac{-2x}{x+2}$ 8) $\frac{x^2+x}{4} : \frac{x^2}{4} + \frac{x-1}{x} = \frac{x(x+1)}{4} \cdot \frac{4}{x^2} + \frac{x-1}{x} = \frac{x+1}{x} + \frac{x-1}{x} = \frac{x+1+x-1}{x} = \frac{2x}{x} = 2$ 9) $\frac{6c^2}{c^2-1} : \left(\frac{1}{c-1} + 1\right) = \frac{6c^2}{(c-1)(c+1)} : \frac{1 + (c-1)}{c-1} = \frac{6c^2}{(c-1)(c+1)} : \frac{c}{c-1} = \frac{6c^2}{(c-1)(c+1)} \cdot \frac{c-1}{c} = \frac{6c}{c+1}$ 10) $\left(\frac{x}{x+y} + \frac{y}{x-y}\right) \cdot \frac{x^2+xy}{x^2+y^2} = \frac{x(x-y) + y(x+y)}{(x+y)(x-y)} \cdot \frac{x(x+y)}{x^2+y^2} = \frac{x^2-xy + xy+y^2}{(x+y)(x-y)} \cdot \frac{x(x+y)}{x^2+y^2} = \frac{x^2+y^2}{(x+y)(x-y)} \cdot \frac{x(x+y)}{x^2+y^2} = \frac{x}{x-y}$