1. \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}=4\)
\(\Leftrightarrow\sqrt{\dfrac{\left(2-\sqrt{3}\right)^2}{1}}+\sqrt{\dfrac{\left(2+\sqrt{3}\right)^2}{1}}=4\)
\(\Leftrightarrow2-\sqrt{3}+2+\sqrt{3}=4\)
\(\Leftrightarrow4=4\left(đpcm\right)\)
2. \(\dfrac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\dfrac{2b}{a-b}=1\)
\(\Leftrightarrow\dfrac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)-\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)-2b}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}=1\)
\(\Leftrightarrow\dfrac{a+\sqrt{ab}-\sqrt{ab}+b-2b}{a-b}1\)
\(\Leftrightarrow\dfrac{a-b}{a-b}=1\left(đpcm\right)\)
