Khi rút gọn biểu thức \(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}+\dfrac{\sqrt{a}^3+\sqrt{b}^3}{a-b}\), ta được kết quả là
\(\dfrac{2a-\sqrt{ab}}{\sqrt{a}-\sqrt{b}}\). \(\sqrt{a}\). \(2\sqrt{a}\). \(\sqrt{a}+\sqrt{b}\). Hướng dẫn giải:\(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}+\dfrac{\sqrt{a}^3+\sqrt{b}^3}{a-b}\)
\(=\sqrt{a}+\sqrt{b}+\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\sqrt{a}+\sqrt{b}+\dfrac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
\(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}+\dfrac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
\(=\dfrac{a-b+a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
\(=\dfrac{2a-\sqrt{ab}}{\sqrt{a}-\sqrt{b}}\)
