Cho \(a>0,b>0,a\ne b\), biểu thức \(N=\frac{a^{\frac{1}{3}}b^{-\frac{1}{3}}-a^{-\frac{1}{3}}b^{\frac{1}{3}}}{\sqrt[3]{a^2}-\sqrt[3]{b^2}}\) rút gọn bằng
\(\sqrt[3]{a}\). \(\sqrt[3]{b}\). \(\frac{1}{\sqrt[3]{ab}}\). \(\sqrt[3]{ab}\). Hướng dẫn giải: \(N=\frac{a^{\frac{1}{3}}b^{-\frac{1}{3}}-a^{-\frac{1}{3}}b^{\frac{1}{3}}}{\sqrt[3]{a^2}-\sqrt[3]{b^2}}=\frac{a^{-\frac{1}{3}}b^{-\frac{1}{3}}\left(a^{\frac{2}{3}}-b^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}-b^{\frac{2}{3}}}\)
\(=a^{-\frac{1}{3}}b^{-\frac{1}{3}}=\frac{1}{\sqrt[3]{ab}}\).