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.