Question

Докажите тождество. Всё на картинке

Answer 1

.$frac{(x-y)^2+xy}{(x-y)^2+xy} ( frac{x^5+y^5+x^3y^2+x^2y^3}{(x^3-y^3)(x^3+y^3+x^2y+xy^2)} )^{-1}equiv \ equiv frac{x^2-xy+y^2}{x^2+xy+y^2} ( frac{x^3(x^2+y^2)+y^3(x^2+y^2)}{(x^3-y^3)(x^2(x+y)+y^2(x+y))} )^{-1}equiv frac{(x-y)(x^3+y^3)}{(x+y)(x^3-y^3)} * \ * frac{(x^3-y^3)(x^2+y^2)(x+y)}{(x^3+y^3)(x^2+y^2)} equiv x-y$