Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\dfrac{{x - 1}}{{\sqrt x }} > 0\\
x > 0 \Rightarrow \sqrt x > 0\\
\Rightarrow x - 1 > 0 \Rightarrow x > 1\\
b,\\
\dfrac{{x - 1}}{{\sqrt x }} = 2\,\,\,\,\,\,\,\,\,\,\,\,\left( {x > 0,x \ne 1} \right)\\
\Leftrightarrow x - 1 = 2\sqrt x \\
\Leftrightarrow x - 1 - 2\sqrt x = 0\\
\Leftrightarrow \left( {x - 2\sqrt x + 1} \right) - 2 = 0\\
\Leftrightarrow {\left( {\sqrt x - 1} \right)^2} - 2 = 0\\
\Leftrightarrow {\left( {\sqrt x - 1} \right)^2} = {\sqrt 2 ^2}\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt x - 1 = \sqrt 2 \\
\sqrt x - 1 = - \sqrt 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt x = \sqrt 2 + 1\\
\sqrt x = - \sqrt 2 + 1
\end{array} \right.\\
\sqrt x > 0 \Rightarrow \sqrt x = \sqrt 2 + 1 \Rightarrow x = {\left( {\sqrt 2 + 1} \right)^2} = 3 + 2\sqrt 2
\end{array}\)
