Rút gọn biểu thức \(C=\dfrac{\left(a^{\dfrac{1}{3}}+b^{\dfrac{1}{3}}\right)^2}{\sqrt[3]{ab}}:\left(2+\sqrt[3]{\dfrac{a}{b}}+\sqrt[3]{\dfrac{b}{a}}\right)\) được kết quả là
\(a+b\).\(1\).\(\sqrt{a}-\sqrt{b}\).\(\dfrac{1}{2}\).Hướng dẫn giải:\(C=\dfrac{\left(a^{\frac{1}{3}}+b^{\frac{1}{3}}\right)^2}{\sqrt[3]{ab}}:\left(2+\sqrt[3]{\dfrac{a}{b}}+\sqrt[3]{\dfrac{b}{a}}\right)\)
\(=\dfrac{\left(\sqrt[3]{a}+\sqrt[3]{b}\right)^2}{\sqrt[3]{ab}}:\dfrac{2\sqrt[3]{ab}+\sqrt[3]{a^2}+\sqrt[3]{b^2}}{\sqrt[3]{ab}}\)
\(=\dfrac{\left(\sqrt[3]{a}+\sqrt[3]{b}\right)^2}{\sqrt[3]{ab}}:\dfrac{\left(\sqrt[3]{a}+\sqrt[3]{b}\right)^2}{\sqrt[3]{ab}}\)
\(=1\)
