Question

Rút gọn:

\(\frac{x\sqrt[3]{y}+\sqrt[3]{x^2y^2}}{\sqrt[3]{x^2y^2}+y\sqrt[3]{x}}\)

\(\frac{\sqrt[3]{54}-2\sqrt[3]{16}}{\sqrt[3]{54}+2\sqrt[3]{16}}\)

Answer 1

a) \(\frac{x\sqrt[3]{y}+\sqrt[3]{x^2y^2}}{\sqrt[3]{x^2y^2}+y\sqrt[3]{x}}\)

\(=\frac{\sqrt[3]{x^2y}\left(\sqrt[3]{x}+\sqrt[3]{y}\right)}{\sqrt[3]{xy^2}\left(\sqrt[3]{x}+\sqrt[3]{y}\right)}=\sqrt[3]{\frac{x^2y}{xy^2}}=\sqrt[3]{\frac{x}{y}}\)

b) \(\frac{\sqrt[3]{54}-2\sqrt[3]{16}}{\sqrt[3]{54}+2\sqrt[3]{16}}\)

\(=\frac{\sqrt[3]{27.2}-2\sqrt[3]{8.2}}{\sqrt[3]{27.2}+2\sqrt[3]{8.2}}\)

\(=\frac{3\sqrt[3]{2}-4\sqrt[3]{2}}{3\sqrt[3]{2}+4\sqrt[3]{2}}=\frac{-\sqrt[3]{2}}{7\sqrt[3]{2}}=-\frac{1}{7}\)