4) `(a\sqrt{a}+b\sqrt{b})/(\sqrt{a}+\sqrt{b})-\sqrt{ab}` `(a>0,b>0)`
`=((\sqrt{a})^3+(\sqrt{b})^3)/(\sqrt{a}+\sqrt{b})-\sqrt{ab}`
`=((\sqrt{a}+\sqrt{b})(a-\sqrt{ab}+b))/(\sqrt{a}+\sqrt{b})-\sqrt{ab}`
`=a-\sqrt{ab}+b-\sqrt{ab}`
`=a-2\sqrt{ab}+b`
`=(\sqrt{a})^2-2.\sqrt{a}.\sqrt{b}+(\sqrt{b})^2`
`=(\sqrt{a}-\sqrt{b})^2`