Question

Thu gọn :

\(\left(\dfrac{a-4b}{\sqrt{a}+2\sqrt{b}}\right):\dfrac{\sqrt{ab}}{a\sqrt{b}+b\sqrt{a}}\)

Answer 1

\(\left(\dfrac{a-4b}{\sqrt{a}+2\sqrt{b}}\right):\dfrac{\sqrt{ab}}{a\sqrt{b}+b\sqrt{a}}\)

=\(\dfrac{\left(\sqrt{a}-2\sqrt{b}\right)\left(\sqrt{a}+2\sqrt{b}\right)}{\sqrt{a}+2\sqrt{b}}:\dfrac{\sqrt{ab}}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)

= (\(\sqrt{a}-2\sqrt{b}\)): \(\dfrac{1}{\sqrt{a}+\sqrt{b}}\)

= \(\left(\sqrt{a}-2\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)\)

= a + \(\sqrt{ab}\)- 2\(\sqrt{ab}\)- 2b

= a - \(\sqrt{ab}\)- 2b