Question

Помогите прошу вас, даю 20 баллов
докажите тождество (m^2/m+5-m3/m2+10m+25):(m/m+5-m^2/m^2-25)=5m-m^2/m+5

Answer 1

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

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

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

$\frac{m^3+5m^2-m^3}{(m+5)^2}: \frac{m(m-5)-m^2}{(m+5)(m-5)}=$

$\frac{5m^2}{(m+5)^2}: \frac{m^2-5m-m^2}{(m+5)(m-5)}=$

$\frac{5m^2}{(m+5)^2}: \frac{-5m}{(m+5)(m-5)}=$

$\frac{5m^2}{(m+5)^2} \cdot \frac{(m+5)(m-5)}{-5m}=$

$\frac{m}{m+5} \cdot \frac{m-5}{-1}=\frac{m(m-5)}{-(m+5)}=\frac{m^2-5m}{-(m+5)}= \frac{5m-m^2}{m+5}$