a, ĐKXD: \(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-1\ne0\\\sqrt{x}+1\ne0\\\sqrt{x}\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\ne1\\\sqrt{x}\ne-1\\\sqrt{x}\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)
\(A=\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}+\dfrac{1}{\sqrt{x}}\)
\(=\dfrac{\left(\sqrt{x}+1\right)\sqrt{x}+\left(\sqrt{x}-1\right)\sqrt{x}+\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\sqrt{x}}\)
\(=\dfrac{x+\sqrt{x}+x-\sqrt{x}+x-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\sqrt{x}}\)
\(=\dfrac{3x-1}{\left(x-1\right)\sqrt{x}}\)
b, Khi \(x=\dfrac{1}{4}\):
\(A=\dfrac{3.\dfrac{1}{4}-1}{\left(\dfrac{1}{4}-1\right)\sqrt{\dfrac{1}{4}}}=\dfrac{\dfrac{3}{4}-1}{-\dfrac{3}{4}.\dfrac{1}{2}}=\dfrac{-\dfrac{1}{4}}{-\dfrac{3}{8}}=\dfrac{2}{3}\)
