Выполни деление алгебраических дробей: 5m-2n/10k : 5m-2n/10k²

Конечно, давай решим эти примеры по порядку! 1) $\frac{5m - 2n}{10k} : \frac{5m - 2n}{10k^2} = \frac{5m - 2n}{10k} \cdot \frac{10k^2}{5m - 2n} = \frac{10k^2(5m - 2n)}{10k(5m - 2n)} = k$ 2) $\frac{p + 3}{p^2 - 2p} : \frac{p + 3}{4p - 8} = \frac{p + 3}{p(p - 2)} \cdot \frac{4(p - 2)}{p + 3} = \frac{4(p + 3)(p - 2)}{p(p - 2)(p + 3)} = \frac{4}{p}$ 3) $\frac{a^2 - b^2}{2ab} : \frac{a + b}{ab} = \frac{(a - b)(a + b)}{2ab} \cdot \frac{ab}{a + b} = \frac{ab(a - b)(a + b)}{2ab(a + b)} = \frac{a - b}{2}$ 4) $\frac{a^2 - 16}{a - 3} : \frac{a + 4}{a - 3} = \frac{(a - 4)(a + 4)}{a - 3} \cdot \frac{a - 3}{a + 4} = \frac{(a - 4)(a + 4)(a - 3)}{(a - 3)(a + 4)} = a - 4$ 5) $\frac{y - 9}{y - 8} : \frac{y^2 - 81}{y^2 - 16y + 64} = \frac{y - 9}{y - 8} \cdot \frac{(y - 8)^2}{y^2 - 81} = \frac{y - 9}{y - 8} \cdot \frac{(y - 8)^2}{(y - 9)(y + 9)} = \frac{(y - 9)(y - 8)^2}{(y - 8)(y - 9)(y + 9)} = \frac{y - 8}{y + 9}$ 6) $(x^2 - 49y^2) : \frac{x - 7y}{x} = (x - 7y)(x + 7y) \cdot \frac{x}{x - 7y} = \frac{x(x - 7y)(x + 7y)}{x - 7y} = x(x + 7y)$ **Ответы:** 1) $k$ 2) $\frac{4}{p}$ 3) $\frac{a - b}{2}$ 4) $a - 4$ 5) $\frac{y - 8}{y + 9}$ 6) $x(x + 7y)$