Question

Помогите доказать тождество k/k-m+m^2-k^2/mk+m^2:m^2-2mk+k^6/k^6=-k/m

Answer 1

$frac{k}{k-m}+frac{m^2-k^2}{mk+m^2}:frac{m^2-2mk+k^2}{k^2}=-frac{k}{m}\ frac{k}{k-m}+frac{(m-k)(m+k)}{m(k+m)}:frac{(m-k)^2}{k^2}=frac{k}{k-m}+frac{(m-k)(m+k)}{m(k+m)}cdotfrac{k^2}{(m-k)^2}=\ =frac{k}{k-m}+frac{k^2}{m(m-k)}=frac{k}{k-m}-frac{k^2}{m(k-m)}=frac{km-k^2}{m(k-m)}=\ =frac{k(m-k)}{m(k-m)}=-frac{k(m-k)}{m(m-k)}=-frac{k}{m}$