Cho biểu thức 

- Hướng dẫn giải

1. Điều kiện $\left\{\begin{array}{l}a>0\\ a\ne 1\end{array}\right.$

Ta có

$\begin{array}{l}A={\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)}^2\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\\ ={\left(\frac{a-1}{2\sqrt{a}}\right)}^2.\left(\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\\ =\frac{{\left(a-1\right)}^2}{4a}.\left(\frac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{a-1}\right)\\ =-\frac{a-1}{\sqrt{a}}\end{array}$