\(\left(\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right).\left(\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2\);\(a,b\ge0;a\ne b\)
\(=\left(\dfrac{a\sqrt{a}+b\sqrt{b}-a\sqrt{b}-b\sqrt{a}}{\sqrt{a}+\sqrt{b}}\right).\left(\dfrac{\sqrt{a}+\sqrt{b}}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\right)^2\)
\(=\left(\dfrac{a\left(\sqrt{a}-\sqrt{b}\right)-b\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}\right).\left(\dfrac{1}{\sqrt{a}-\sqrt{b}}\right)^2\)
\(=\left(\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(a-b\right)}{\sqrt{a}+\sqrt{b}}\right).\left(\dfrac{1}{\sqrt{a}-\sqrt{b}}\right)^2\)
\(=\left(\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}\right).\left(\dfrac{1}{\sqrt{a}-\sqrt{b}}\right)^2\)
\(=\left(\sqrt{a}-\sqrt{b}\right)^2.\dfrac{1}{\left(\sqrt{a}-\sqrt{b}\right)^2}\)
\(=1\left(đfcm\right)\)
