Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ne y \ne 0\\
x \ne - y
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
A = \left( {\frac{1}{x} - \frac{1}{y}} \right)\left( {\frac{{x - y}}{{x + y}} - \frac{{x + y}}{{x - y}}} \right)\\
= \frac{{y - x}}{{xy}}.\frac{{{{\left( {x - y} \right)}^2} - {{\left( {x + y} \right)}^2}}}{{\left( {x - y} \right).\left( {x + y} \right)}}\\
= \frac{{y - x}}{{xy}}.\frac{{{x^2} - 2xy + {y^2} - {x^2} - 2xy - {y^2}}}{{\left( {x - y} \right)\left( {x + y} \right)}}\\
= \frac{{\left( {y - x} \right).\left( { - 4xy} \right)}}{{xy.\left( {x - y} \right)\left( {x + y} \right)}}\\
= \frac{{4xy.\left( {x - y} \right)}}{{xy.\left( {x - y} \right)\left( {x + y} \right)}}\\
= \frac{4}{{x + y}}
\end{array}\)
