1.
\(A=\dfrac{y-x}{xy}:\left[\dfrac{y^2}{\left(x-y\right)^2}-\dfrac{2x^2y}{\left(x+y\right)^2\left(x-y\right)^2}-\dfrac{x^2}{\left(x-y\right)\left(x+y\right)}\right]\)
\(=\dfrac{y-x}{xy}:\left[\dfrac{y^2}{\left(x-y\right)^2}-\dfrac{2x^2y}{\left(x-y\right)^2}-\dfrac{x^2\left(x-y\right)}{\left(x-y\right)^2}\right]\)
\(=\dfrac{y-x}{xy}:\left[\dfrac{y^2-2x^2y-x^2\left(x-y\right)}{\left(x-y\right)^2}\right]\)
\(=\dfrac{y-x}{xy}:\left[\dfrac{y^2-x^2y-x^3}{\left(x-y\right)^2}\right]=\dfrac{y-x}{xy}:\left[\dfrac{y^2-x^2\left(1-x\right)-x^3}{\left(x-y\right)^2}\right]\)
\(=\dfrac{y-x}{xy}:\left[\dfrac{y^2-x^2}{\left(x-y\right)^2}\right]=\dfrac{y-x}{xy}:\left[\dfrac{\left(y-x\right)\left(y+x\right)}{\left(x-y\right)^2}\right]\)
\(=\dfrac{\left(y-x\right)}{xy}.\dfrac{\left(x-y\right)^2}{\left(y-x\right)}=\dfrac{\left(x-y\right)^2}{xy}\)
b,
\(A=\dfrac{x^2-2xy+y^2}{xy}=\dfrac{x^2+2xy+y^2-4xy}{xy}=\dfrac{\left(x+y\right)^2}{xy}-4\)
\(=\dfrac{1}{xy}-4\)
Do \(x>0;y< 0\Rightarrow xy< 0\Leftrightarrow\dfrac{1}{xy}< 0\)
\(\Rightarrow\dfrac{1}{xy}-4< -4\Rightarrow A< -4\)
