Question

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

Answer 1

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