сократите дробь: u^3-u^2v+uv^2-v^3 ________________ u^4v^2-v^6

сократите дробь: u^3-u^2v+uv^2-v^3 ________________ u^4v^2-v^6

Ответ:

u^3-u^2v+uv^2-v^3 _______________ u^4v^2-v^6 = (u^2(u - v) + v^2(u - v)) / v^2(u^4 - v^4))= = ((u - v)(u^2 + v^2)) / v^2(u^2 - v^2)(u^2 + v^2)) = (u - v) / v^2(u^2 - v^2)) = = (u - v) / v^2(u - v)(u + v)) = 1 / v^2(u + v))

Источник: https://znanija.com/task/46714