Question

Срочно! Отдаю 40 баллов! Алгебра 8 класс! Задание на картинке!

Answer 1

Решение:

$1)~ \dfrac{m^2- 5 m + 25}{25m^2-1}\cdot \dfrac{5m^2 + m}{m^3 + 125} = \\\\ =\dfrac{m^2- 5 m + 25}{(5m-1)(5m + 1)}\cdot \dfrac{m(5m + 1)}{(m + 5)(m^2- 5 m + 25)} =\dfrac{m}{(5m - 1)(m + 5)}$

$2)~\dfrac{m}{(5m - 1)(m + 5)} - \dfrac{m+5}{5m^2 - m} = \dfrac{m}{(5m - 1)(m + 5)} - \dfrac{m+5}{m(5m - 1)} =\\ \\ = \dfrac{m^2- (m + 5)^2}{m(5m-1)(m+5)} = \dfrac{m^2- m^2 - 10m -25 }{m(5m-1)(m+5)} = \dfrac{ 10m +25 }{m(1-5m)(m+5)}$

$3)~\dfrac{10m + 25}{m(1-5m)(m+5)}: \dfrac{7}{m^2+5m} =\\\\= \dfrac{(10m + 25)m(m+5)}{7m(1-5m)(m+5)}= \dfrac{10m + 25}{7(1 - 5m)}$

$4) ~\dfrac{10m +25}{7(1 - 5m)} - \dfrac{25m + 22}{7 - 35m} =\dfrac{10m + 25}{7(1 - 5m)} - \dfrac{25m + 22}{7(1 - 5m)} =\\\\=\dfrac{10m + 25-25m - 22}{7(1 - 5m)} =\dfrac{3-15m}{7(1 - 5m)} =\dfrac{3-15m}{7 - 35m}$