алгебра

[paris]

[tex]\frac{(x^{2}-y^{2})(\sqrt[3]{x}+\sqrt[3]{y}) }{ \sqrt[3]{x^{5}}+\sqrt[3]{x^{2}.y^{3}}-\sqrt[3]{x^{3}.y^{2}}-\sqrt[3]{y^{5}} }[/tex] - [tex](\sqrt[3]{x.y}+\sqrt[3]{y^{2}})[/tex]=?

Мерси предварително за помощта

[math10.com]

[tex]\frac{(x^2-y^2)(\sqrt[3]{x}+\sqrt[3]{y})}{\sqrt[3]{x^5}+\sqrt[3]{x^2y^3} -\sqrt[3]{x^3y^2} -\sqrt[3]{y^5} }-(\sqrt[3]{xy}+ \sqrt[3]{y^2})= \frac{(x-y)(x+y)(\sqrt[3]{x}+\sqrt[3]{y})}{\sqrt[3]{x^2}(\sqrt[3]{x^3} +\sqrt[3]{y^3}) -\sqrt[3]{y^2}(\sqrt[3]{x^3} +\sqrt[3]{y^3} ) }-(\sqrt[3]{xy}+ \sqrt[3]{y^2})[/tex]

[tex]=\frac{(x-y)(x+y)(\sqrt[3]{x}+\sqrt[3]{y})}{(\sqrt[3]{x^2}-\sqrt[3]{y^2})(x +y)} -(\sqrt[3]{xy}+ \sqrt[3]{y^2})=\frac{(x-y)\cancel{(x+y)}\cancel{(\sqrt[3]{x}+\sqrt[3]{y})}}{\cancel{(\sqrt[3]{x}+\sqrt[3]{y})}(\sqrt[3]{x}-\sqrt[3]{y})\cancel{(x +y)}} -(\sqrt[3]{xy}+ \sqrt[3]{y^2})[/tex]

[tex]=\frac{\cancel{(\sqrt[3]{x}-\sqrt[3]{y})}(\sqrt[3]{x^2}+\sqrt[3]{xy} +\sqrt[3]{y^2})}{\cancel{(\sqrt[3]{x}-\sqrt[3]{y})}}-(\sqrt[3]{xy}+ \sqrt[3]{y^2})=\sqrt[3]{x^2}+\cancel{\sqrt[3]{xy}} +\cancel{\sqrt[3]{y^2}}-\cancel{\sqrt[3]{xy}}-\cancel{\sqrt[3]{y^2}}=\sqrt[3]{x^2}[/tex]

Допустимите стойности са [tex]|x|\ne|y|[/tex]