Đáp án:
$\begin{array}{l}
x = \dfrac{{4 - \sqrt 7 }}{2}\left( {tmdk} \right)\\
x = \dfrac{{8 - 2\sqrt 7 }}{4} = \dfrac{{{{\left( {\sqrt 7 - 1} \right)}^2}}}{4}\\
\Rightarrow \sqrt x = \dfrac{{\sqrt 7 - 1}}{2}\\
\Rightarrow A = \dfrac{1}{{\sqrt x }} + \dfrac{{\sqrt x }}{{\sqrt x + 1}}\\
= \dfrac{2}{{\sqrt 7 - 1}} + \dfrac{{\dfrac{{\sqrt 7 - 1}}{2}}}{{\dfrac{{\sqrt 7 - 1}}{2} + 1}}\\
= \dfrac{{2\left( {\sqrt 7 + 1} \right)}}{{7 - 1}} + \dfrac{{\sqrt 7 - 1}}{{\sqrt 7 - 1 + 2}}\\
= \dfrac{{\sqrt 7 + 1}}{3} + \dfrac{{\sqrt 7 - 1}}{{\sqrt 7 + 1}}\\
= \dfrac{{\sqrt 7 + 1}}{3} + \dfrac{{{{\left( {\sqrt 7 - 1} \right)}^2}}}{{7 - 1}}\\
= \dfrac{{2\sqrt 7 + 2 + 8 - 2\sqrt 7 }}{6}\\
= \dfrac{{10}}{6} = \dfrac{5}{3}
\end{array}$
