Giải thích các bước giải:
Ta có:
a,
\(\begin{array}{l}
A = \frac{{y - x}}{{xy}}:\left[ {\frac{{{y^2}}}{{{{\left( {x - y} \right)}^2}}} - \frac{{2{x^2}y}}{{{{\left( {{x^2} - {y^2}} \right)}^2}}} + \frac{{{x^2}}}{{{y^2} - {x^2}}}} \right]\\
= \frac{{y - x}}{{xy}}:\left[ {\frac{{{y^2}}}{{{{\left( {x - y} \right)}^2}}} - \frac{{2{x^2}y}}{{{{\left( {x - y} \right)}^2}{{\left( {x + y} \right)}^2}}} + \frac{{{x^2}}}{{\left( {y - x} \right)\left( {y + x} \right)}}} \right]\\
= \frac{{y - x}}{{xy}}:\left[ {\frac{{{y^2}}}{{{{\left( {x - y} \right)}^2}}} - \frac{{2{x^2}y}}{{{{\left( {x - y} \right)}^2}}} - \frac{{{x^2}}}{{x - y}}} \right]\\
= \frac{{y - x}}{{xy}}:\left[ {\frac{{{y^2} - 2{x^2}y - {x^2}\left( {x - y} \right)}}{{{{\left( {x - y} \right)}^2}}}} \right]\\
= \frac{{y - x}}{{xy}}:\left[ {\frac{{{y^2} - {x^2}y - {x^3}}}{{{{\left( {x - y} \right)}^2}}}} \right]\\
= \frac{{y - x}}{{xy}}:\frac{{{y^2} - {x^2}\left( {x + y} \right)}}{{{{\left( {x - y} \right)}^2}}}\\
= \frac{{y - x}}{{xy}}:\frac{{{y^2} - {x^2}}}{{{{\left( {x - y} \right)}^2}}}\\
= \frac{{y - x}}{{xy}}:\frac{{x + y}}{{y - x}} = \frac{{{{\left( {y - x} \right)}^2}}}{{xy}}\\
b,\\
A + 4 = \frac{{{{\left( {y - x} \right)}^2}}}{{xy}} + 4 = \frac{{{x^2} - 2xy + {y^2} + 4xy}}{{xy}} = \frac{{{{\left( {x + y} \right)}^2}}}{{xy}}\\
x > 0,\,\,\,y < 0 \Rightarrow xy < 0\\
\Rightarrow A + 4 < 0 \Leftrightarrow A < - 4
\end{array}\)
