Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\dfrac{1}{{5 - \sqrt 3 }} - \dfrac{1}{{5 + \sqrt 3 }} = \dfrac{{\left( {5 + \sqrt 3 } \right) - \left( {5 - \sqrt 3 } \right)}}{{\left( {5 - \sqrt 3 } \right).\left( {5 + \sqrt 3 } \right)}} = \dfrac{{2\sqrt 3 }}{{{5^2} - {{\sqrt 3 }^2}}} = \dfrac{{2\sqrt 3 }}{{22}} = \dfrac{{\sqrt 3 }}{{11}}\\
b,\\
\dfrac{{x + 1}}{{x + 2}}:\dfrac{{x + 2}}{{x + 3}}:\dfrac{{x + 3}}{{x + 1}}\,\,\,\,\,\,\left( {x \ne - 1;\,\,x \ne - 2;\,\,\,x \ne - 3} \right)\\
= \dfrac{{x + 1}}{{x + 2}}.\dfrac{{x + 3}}{{x + 2}}.\dfrac{{x + 1}}{{x + 3}}\\
= \dfrac{{{{\left( {x + 1} \right)}^2}}}{{{{\left( {x + 2} \right)}^2}}} = {\left( {\dfrac{{x + 1}}{{x + 2}}} \right)^2}
\end{array}\)