\(\left(\dfrac{\sqrt{b}}{a-\sqrt{ab}}-\dfrac{\sqrt{a}}{\sqrt{ab}-b}\right).\left(a\sqrt{b}-b\sqrt{a}\right)\)
= \(\dfrac{\sqrt{b}\left(a\sqrt{b}-b\sqrt{a}\right)}{a-\sqrt{ab}}\)-\(\dfrac{\sqrt{a}\left(a\sqrt{b}-b\sqrt{a}\right)}{\sqrt{ab}-b}\)
= \(\dfrac{\sqrt{b^2}a-b\sqrt{ab}}{a-\sqrt{ab}}-\dfrac{a\sqrt{ab}-b\sqrt{a^2}}{\sqrt{ab}-b}\)
= \(\dfrac{ab-b\sqrt{ab}}{a-\sqrt{ab}}-\dfrac{a\sqrt{ab}-ab}{\sqrt{ab}-b}\)
= \(\dfrac{b\left(a-\sqrt{ab}\right)}{a-\sqrt{ab}}-\dfrac{a\left(\sqrt{ab}-b\right)}{\sqrt{ab}-b}\)
= b-a
Cách 2: bn hiểu cách nào thì lm cách đó nha
\(\left(\dfrac{\sqrt{b}}{a-\sqrt{ab}}-\dfrac{\sqrt{a}}{\sqrt{ab}-b}\right).\left(a\sqrt{b}-b\sqrt{a}\right)\)
= \(\left(\dfrac{\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}-\dfrac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}\right).\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
= \(\left(\dfrac{b}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}-\dfrac{a}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\right).\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
= \(\dfrac{\left(b-a\right)\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\)
= b-a
