\(ĐK:a\ge0;a\ne0;a\ne1\)
\(A=\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)\left(\frac{a-\sqrt{a}}{\sqrt{a}+1}-\frac{a+\sqrt{a}}{\sqrt{a}-1}\right)=\left(\frac{a}{2\sqrt{a}}-\frac{1}{2\sqrt{a}}\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}+1}-\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}-1}\right)=\sqrt{a}\left(\frac{a-1}{2\sqrt{a}}\right)\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}+\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)=\sqrt{a}\left(\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{2\sqrt{a}}\right)\left(\frac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+\frac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)\(A=\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{2}.\left(\frac{a-2\sqrt{a}+1}{a-1}+\frac{a+2\sqrt{a}+1}{a-1}\right)=\frac{a-1}{2}.\frac{2a+2}{a-1}=\frac{2a+2}{2}=a+1\)
\(A=-4\Leftrightarrow a+1=-4\Leftrightarrow a=-5\left(loại\right)\)
