`M` $=\left(\dfrac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}} + \dfrac{2b}{\sqrt{a}+\sqrt{b}}\right )$ `.` $\left(\dfrac{1}{\sqrt{a}} + \dfrac{1}{\sqrt{b}} \right)$
`=` $\left(\dfrac{(a\sqrt{a}-b\sqrt{b})(\sqrt{a}+\sqrt{b})+2b(a+b+\sqrt{ab})}{(a+b+\sqrt{ab})(\sqrt{a}+\sqrt{b})}\right)$ . $\dfrac{\sqrt{a}+\sqrt{b}}{\sqrt{ab}}$
`=`$\dfrac{a^2+a\sqrt{ab}-b\sqrt{ab}-b^2+2ab+2b^2+2b\sqrt{ab}}{\left(a+b+\sqrt{ab}\right)\sqrt{ab}}$
`=`$\dfrac{(a+b)^2+\sqrt{ab}(a+b)}{\left(a+b+\sqrt{ab}\right)\sqrt{ab}}$
`=`$\dfrac{a+b}{\sqrt{ab}}$
Vâỵ `M` `=` $\dfrac{a+b}{\sqrt{ab}}$ với `a,bgt0`
Chúc bạn học tốt !!🙆
@Katniss
