Ta có: \(\left(\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}+\frac{a}{b-a}\right):\left(\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}+\frac{a}{a+b+2\sqrt{ab}}\right)\)
\(=\left(\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}-\frac{a}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\right):\left(\frac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}+\sqrt{b}\right)^2}+\frac{a}{\left(\sqrt{a}+\sqrt{b}\right)^2}\right)\)
\(=\left(\frac{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}-\frac{a}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\right):\left(\frac{a+\sqrt{ab}+a}{\left(\sqrt{a}+\sqrt{b}\right)^2}\right)\)
\(=\frac{a-\sqrt{ab}-a}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}:\frac{2\sqrt{a}+\sqrt{ab}}{\left(\sqrt{a}+\sqrt{b}\right)^2}\)
\(=\frac{-\sqrt{ab}}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\cdot\frac{\left(\sqrt{a}+\sqrt{b}\right)^2}{\sqrt{a}\left(2+\sqrt{b}\right)}\)
\(=\frac{-\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{b}+2\right)}\)
