Đáp án:
$\displaystyle M=\frac{3\left(\sqrt{a} -\sqrt{b}\right)}{2}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} M=\frac{a+b}{\sqrt{a} +\sqrt{b}} .\frac{\sqrt{ab}\left(\sqrt{a} -\sqrt{b}\right)\left(\sqrt{a} +\sqrt{b}\right)}{( a+b)\sqrt{ab} +b\left(\sqrt{a} +\sqrt{b}\right)\sqrt{a} +a\left(\sqrt{a} -\sqrt{b}\right)\sqrt{b}} -\frac{\sqrt{b} -\sqrt{a}}{2}\\ ( \ do\ b >a >0)\\ M=\frac{a+b}{\sqrt{a} +\sqrt{b}} .\frac{\sqrt{ab}\left(\sqrt{a} -\sqrt{b}\right)\left(\sqrt{a} +\sqrt{b}\right)}{a\sqrt{ab} +b\sqrt{ab} +ab+b\sqrt{ab} +a\sqrt{ab} -ab} -\frac{\sqrt{b} -\sqrt{a}}{2}\\ M=\frac{a+b}{\sqrt{a} +\sqrt{b}} .\frac{\sqrt{ab}\left(\sqrt{a} -\sqrt{b}\right)\left(\sqrt{a} +\sqrt{b}\right)}{2\left( a\sqrt{ab} +b\sqrt{ab}\right)} -\frac{\sqrt{b} -\sqrt{a}}{2}\\ M=\frac{a+b}{\sqrt{a} +\sqrt{b}} .\frac{\sqrt{ab}\left(\sqrt{a} -\sqrt{b}\right)\left(\sqrt{a} +\sqrt{b}\right)}{2\sqrt{ab}( a+b)} -\frac{\sqrt{b} -\sqrt{a}}{2}\\ M=\left(\sqrt{a} -\sqrt{b}\right) -\frac{\sqrt{b} -\sqrt{a}}{2}\\ M=\frac{2\sqrt{a} -2\sqrt{b} -\sqrt{b\ } +\sqrt{a}}{2}\\ M=\frac{3\left(\sqrt{a} -\sqrt{b}\right)}{2} \end{array}$
