Question

Trục căn thức ở mẫu

\(\frac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)

Answer 1

\(\frac{\left(\sqrt{a}\right)^3-\left(\sqrt{b}\right)^3}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{\sqrt{a}-\sqrt{b}}\\ \)

\(a+\sqrt{ab}+b\)

Answer 2

Ta có:

\(\frac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}\)

\(\Leftrightarrow\frac{\sqrt{a}^3-\sqrt{b}^3}{\sqrt{a}-\sqrt{b}}\)

\(\Leftrightarrow\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{\sqrt{a}-\sqrt{b}}\)

\(\Rightarrow a+\sqrt{ab}+b\)