Question

Разложи на множители u2-v2/u2-2uv+v2

Answer 1

${u}^{2} - \frac{v^{2}}{u^{2}} - 2uv + v^{2} = (u - v)^{2} - (\frac{v}{u})^{2} = \\ (u - v + \frac{v}{u})(u - v - \frac{v}{u}) = \\ ( \frac{u(u - v) + v}{u})( \frac{u(u - v) - v}{u}) = \\ (\frac{u^{2} - uv + v}{u})( \frac{u^{2} - uv - v}{u})$