Question

rút gọn biểu thức

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

Answer 1

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

\(=\frac{a-b}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\cdot\left(\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\right)\)

\(=a-b\)

Answer 2

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

\(=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}-\frac{\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}\right)\cdot\left[\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\right]\)

\(=\frac{a-b}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\cdot\left[\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\right]\)

\(=\frac{a-b}{1}=a-b\)