a) \(A=\left(1-\frac{1}{\sqrt{a}}\right)\left(\frac{1}{\sqrt{a}-1}+\frac{1}{\sqrt{a}+1}\right)\)
\(\Rightarrow A=\left(\frac{\sqrt{a}}{\sqrt{a}}-\frac{1}{\sqrt{a}}\right)\left(\frac{\sqrt{a}+1+\sqrt{a}-1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)
\(\Rightarrow A=\frac{\sqrt{a}-1}{\sqrt{a}}.\frac{2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)
\(\Rightarrow A=\frac{2}{\sqrt{a}+1}\)
b) Khi \(a=3-2\sqrt{2}\)
\(\Rightarrow A=\frac{2}{\sqrt{3-2\sqrt{2}}+1}\)
\(\Rightarrow A=\frac{2}{\sqrt{\left(\sqrt{2}-1\right)^2}+1}\)
\(\Rightarrow A=\frac{2}{\left|\sqrt{2}-1\right|+1}\)
\(\Rightarrow A=\frac{2}{\sqrt{2}-1+1}\)
\(\Rightarrow A=\frac{2}{\sqrt{2}}\)
\(\Rightarrow A=\frac{2\sqrt{2}}{2}\)
\(\Rightarrow A=\sqrt{2}\)
