\(\frac{\left(\sqrt{a}\right)^3-\left(\sqrt{b}\right)^3}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{\sqrt{a}-\sqrt{b}}\\ \)
\(a+\sqrt{ab}+b\)
Ta có:
\(\frac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)
\(\Leftrightarrow\frac{\sqrt{a}^3-\sqrt{b}^3}{\sqrt{a}-\sqrt{b}}\)
\(\Leftrightarrow\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{\sqrt{a}-\sqrt{b}}\)
\(\Rightarrow a+\sqrt{ab}+b\)