1, đk a ; b > 0
\(\dfrac{a+2\sqrt{ab}+b-\left(a-2\sqrt{ab}+b\right)}{2\left(a-b\right)}+\dfrac{2b-2\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}{a-b}\)
\(=\dfrac{4\sqrt{ab}}{2\left(a-b\right)}+\dfrac{-4\sqrt{ab}}{2\left(ab\right)}=0\)
2, đk a ; b > 0
\(=\left(\dfrac{a\sqrt{a}+b\sqrt{b}-a\sqrt{b}-b\sqrt{a}}{\sqrt{a}+\sqrt{b}}\right)\left(\sqrt{a}-\sqrt{b}\right)^2\)
\(=\dfrac{\left(a-b\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}\left(\sqrt{a}-\sqrt{b}\right)^2=\left(\sqrt{a}-\sqrt{b}\right)^4\)
3,đk a ; b > 0
\(=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}\left(\sqrt{a}+\sqrt{b}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)=a-b\)
