\(D=\left[\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right]:\left(a-b\right)\)
\(=\left(a-2\sqrt{ab}+b\right):\left(a-b\right)\)
\(=\left(\sqrt{a}-\sqrt{b}\right)^2:\left[\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)\right]\)
\(=\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
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