a, Khi x = 16 thì \(A=\dfrac{\sqrt{10}+1}{\sqrt{10}-1}=\dfrac{\left(\sqrt{10}+1\right)^2}{\left(\sqrt{10}-1\right)\left(\sqrt{10}+1\right)}\)
\(=\dfrac{10+2\sqrt{10}+1}{10-1}=\dfrac{11+2\sqrt{10}}{9}\)
b, \(B=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\right)\div\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\dfrac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\div\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\dfrac{\left(\sqrt{x}+1-\sqrt{x}+1\right)\left(\sqrt{x}+1+\sqrt{x}-1\right)}{x-1}.\dfrac{\sqrt{x}-1}{\sqrt{x}}\)
\(=\dfrac{2.2\sqrt{x}}{x-1}.\dfrac{\sqrt{x}-1}{\sqrt{x}}\)\(=\dfrac{4}{\sqrt{x}+1}\)
