Đáp án:
\(x = \dfrac{4}{9}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)P = \left[ {\dfrac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}} - \dfrac{{x - 1}}{{\sqrt x - 1}}} \right]:\dfrac{{\sqrt x \left( {\sqrt x - 1} \right) + \sqrt x }}{{\sqrt x - 1}}\\
= \dfrac{{x - \sqrt x + 1 - x + 1}}{{\sqrt x - 1}}.\dfrac{{\sqrt x - 1}}{{x - \sqrt x + \sqrt x }}\\
= \dfrac{{2 - \sqrt x }}{x}\\
2)P = 3\\
\to \dfrac{{2 - \sqrt x }}{x} = 3\\
\to 3x = 2 - \sqrt x \\
\to 3x + \sqrt x - 2 = 0\\
\to \left( {3\sqrt x - 2} \right)\left( {\sqrt x + 1} \right) = 0\\
\to 3\sqrt x - 2 = 0\\
\to \sqrt x = \dfrac{2}{3}\\
\to x = \dfrac{4}{9}
\end{array}\)
