Ta có :
\(\left(\dfrac{a+\sqrt{a}}{1+\sqrt{a}}+\dfrac{a}{1-\sqrt{a}}\right)\left(\dfrac{a}{2\sqrt{a}}-\dfrac{1}{2}\right)\)
\(=\) \(\left[\dfrac{\left(a+\sqrt{a}\right)\left(1-\sqrt{a}\right)}{1-\sqrt{a}}+\dfrac{a\left(\sqrt{a}+1\right)}{1-\sqrt{a}}\right].\left(\dfrac{a}{2\sqrt{a}}-\dfrac{\sqrt{a}}{2\sqrt{a}}\right)\)
\(=\) \(\left(\dfrac{a-a\sqrt{a}+\sqrt{a}-a+a\sqrt{a}+a}{1-a}\right)\left(\dfrac{a-\sqrt{a}}{2\sqrt{a}}\right)\)
\(=\) \(\dfrac{a-\sqrt{a}}{1-\sqrt{a}}.\dfrac{a-\sqrt{a}}{2\sqrt{a}}\)
\(=\) \(\dfrac{a^2-a}{2\sqrt{a}-2a}\)
\(=\) \(\dfrac{a\left(a-\sqrt{a}\right)}{-2\left(a-\sqrt{a}\right)}\)
\(=\) \(\dfrac{-a}{2}\)
