Докажите тождество: k/(k-m)+(m^2-k^2)/(mk+m^2):(m^2-2mk+k^2)/k^2=-k/m.

\[1)\ \frac{m^{2} - k^{2}}{mk + m^{2}}\ :\frac{m^{2} - 2mk + k^{2}}{k^{2}} =\]

\[= \frac{m^{2} - k^{2}}{mk + m^{2}} \cdot \frac{k^{2}}{m^{2} - 2mk + k^{2}} =\]

\[= \frac{(m - k)(m + k)k^{2}}{m(k + m)(m - k)^{2}} =\]

\[= \frac{k^{2}}{m(m - k)} = \frac{k^{2}}{m^{2} - mk}.\]