Question

Помогите с 21 пожалуйста

Answer 1

(∛x+∛y)/(∛x²-∛xy +∛y²)-(∛x-∛y)/(∛x-∛y)(∛x+∛y)=
=(∛x+∛y)/(∛x²-∛xy +∛y²)- 1/(∛x+∛y)=
[(∛x+∛y)²-(∛x²-∛xy +∛y²)]/(∛x-∛y)(∛x+∛y)=
=(∛x²+2∛xy +∛y²-∛x²+∛xy -∛y²)/(x+y)=3∛xy/(x+y)

Answer 2

$cfrac{sqrt[3]{x}+sqrt[3]{y}}{x^{frac{2}{3}}-sqrt[3]{xy}+y^{frac{2}{3}}}-cfrac{sqrt[3]{x}-sqrt[3]{y}}{sqrt[3]{x^2}-sqrt[3]{y^2}}=cfrac{sqrt[3]{x}+sqrt[3]{y}}{x^{frac{2}{3}}-sqrt[3]{xy}+y^{frac{2}{3}}}-cfrac{1}{sqrt[3]{x}+sqrt[3]{y}}=\\\cfrac{(sqrt[3]{x}+sqrt[3]{y})^2}{(sqrt[3]{x}+sqrt[3]{y})(x^{frac{2}{3}}-sqrt[3]{xy}+y^{frac{2}{3}})}-cfrac{x^{frac{2}{3}}-sqrt[3]{xy}+y^{frac{2}{3}}}{(sqrt[3]{x}+sqrt[3]{y})(x^{frac{2}{3}}-sqrt[3]{xy}+y^{frac{2}{3}})}=$$cfrac{(sqrt[3]{x})^2+2sqrt[3]{x}sqrt[3]{y}+(sqrt[3]{y})^2-(x^{frac{2}{3}}-sqrt[3]{xy}+y^{frac{2}{3}})}{(sqrt[3]{x})^3+(sqrt[3]{y})^3}=\\\cfrac{(sqrt[3]{x})^2+2sqrt[3]{xy}+(sqrt[3]{y})^2-x^{frac{2}{3}}+sqrt[3]{xy}-y^{frac{2}{3}}}{x+y}=cfrac{3sqrt[3]{xy}}{x+y}$