Đáp án:
\(\left[ \begin{array}{l}
A = \dfrac{{\sqrt 6 }}{{x - y}}\\
A = - \dfrac{{\sqrt 6 }}{{x - y}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \pm y\\
A = \dfrac{2}{{\left( {x - y} \right)\left( {x + y} \right)}}.\dfrac{{\left| {x + y} \right|.\sqrt 3 }}{{\sqrt 2 }}\\
\to \left[ \begin{array}{l}
A = \dfrac{2}{{\left( {x - y} \right)\left( {x + y} \right)}}.\dfrac{{\left( {x + y} \right).\sqrt 3 }}{{\sqrt 2 }}\left( {DK:x \ge - y} \right)\\
A = \dfrac{2}{{\left( {x - y} \right)\left( {x + y} \right)}}.\dfrac{{ - \left( {x + y} \right).\sqrt 3 }}{{\sqrt 2 }}\left( {DK:x < - y} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
A = \dfrac{{\sqrt 6 }}{{x - y}}\\
A = - \dfrac{{\sqrt 6 }}{{x - y}}
\end{array} \right.
\end{array}\)
