\(\left[\dfrac{\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}-\dfrac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}\right].\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left[\dfrac{\sqrt{b}.\sqrt{b}-\sqrt{a}.\sqrt{a}}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\right].\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
=\(\left[\dfrac{b-a}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\right].\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\dfrac{\left(b-a\right).\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\)
=b-a