Question

Докажите пожалуйста.

Answer 1

Доказать тождество.

$\left(\dfrac{m^2}{m+5} - \dfrac{m^3}{m^2+10m+25}\right):\left(\dfrac{m}{m+5} - \dfrac{m^2}{m^2-25}\right) = \dfrac{5m-m^2}{m+5};$

$\left(\dfrac{m^2}{m+5} - \dfrac{m^3}{(m + 5)^2}\right):\left(\dfrac{m}{m+5} - \dfrac{m^2}{(m - 5)(m + 5)}\right) = \dfrac{5m-m^2}{m+5};$

$\left(\dfrac{m^2(m+5)-m^3}{(m + 5)^2}\right):\left(\dfrac{m(m-5)-m^2}{(m - 5)(m + 5)}\right) = \dfrac{5m-m^2}{m+5};$

$\left(\dfrac{m^2((m+5)-m)}{(m + 5)^2}\right):\left(\dfrac{m((m-5)-m)}{(m - 5)(m + 5)}\right) = \dfrac{5m-m^2}{m+5};$

$\left(\dfrac{5m^2}{(m + 5)^2}\right):\left(\dfrac{-5m}{(m - 5)(m + 5)}\right) = \dfrac{5m-m^2}{m+5};$

$\left(\dfrac{5m^2}{(m + 5)^2}\right)*\left(\dfrac{(m - 5)(m + 5)}{-5m}\right) = \dfrac{5m-m^2}{m+5};$

$\dfrac{5m^2(m - 5)(m + 5)}{-5m(m + 5)^2} = \dfrac{5m-m^2}{m+5};$

$\dfrac{-m(m - 5)}{m + 5} = \dfrac{5m-m^2}{m+5};$

$\dfrac{m(5 - m)}{m + 5} = \dfrac{5m-m^2}{m+5};$

$\dfrac{5m - m^2}{m + 5} = \dfrac{5m-m^2}{m+5}.$

Что и требовалось доказать.