Đáp án:
\(\frac{{ - 4}}{{x + 2\sqrt x }}\)
Giải thích các bước giải:
\(\begin{array}{l}
\left( {\frac{1}{{\sqrt x + 2}} - \frac{1}{{\sqrt x - 2}}} \right).\frac{{\sqrt x - 2}}{{\sqrt x }}\\
= \left( {\frac{{\sqrt x - 2}}{{(\sqrt x + 2)(\sqrt x - 2)}} - \frac{{\sqrt x + 2}}{{(\sqrt x + 2)(\sqrt x - 2)}}} \right).\frac{{\sqrt x - 2}}{{\sqrt x }}\\
= \frac{{\sqrt x - 2 - \sqrt x - 2}}{{(\sqrt x + 2)(\sqrt x - 2)}}.\frac{{\sqrt x - 2}}{{\sqrt x }}\\
= \frac{{ - 4}}{{(\sqrt x + 2)(\sqrt x - 2)}}.\frac{{\sqrt x - 2}}{{\sqrt x }}\\
= \frac{{ - 4}}{{\sqrt x (\sqrt x + 2)}}\\
= \frac{{ - 4}}{{x + 2\sqrt x }}
\end{array}\)
