1: \(A=\dfrac{x-y}{xy}:\left[\dfrac{y^2}{\left(x-y\right)^2\left(x+y\right)}-\dfrac{2x^2y}{\left(x^2-y^2\right)^2}-\dfrac{x^2}{\left(x^2-y^2\right)\left(x+y\right)}\right]\)
\(=\dfrac{x-y}{xy}:\left[\dfrac{y^2}{\left(x-y\right)^2\left(x+y\right)}-\dfrac{2x^2y}{\left(x-y\right)^2\cdot\left(x+y\right)^2}-\dfrac{x^2}{\left(x-y\right)\left(x+y\right)^2}\right]\)
\(=\dfrac{x-y}{xy}:\left[\dfrac{y^2\left(x+y\right)-2x^2y-x^2\left(x-y\right)}{\left(x-y\right)^2\left(x+y\right)^2}\right]\)
\(=\dfrac{x-y}{xy}\cdot\dfrac{\left(x-y\right)^2\left(x+y\right)^2}{xy^2+y^3-2x^2y-x^3+x^2y}\)
\(=\dfrac{x-y}{xy}\cdot\dfrac{\left(x-y\right)^2\cdot\left(x+y\right)^2}{xy^2-x^2y-\left(x^3-y^3\right)}\)
\(=\dfrac{x-y}{xy}\cdot\dfrac{\left(x-y\right)^2\cdot\left(x+y\right)^2}{-xy\left(x-y\right)-\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x-y}{xy}\cdot\dfrac{\left(x-y\right)^2\left(x+y\right)^2}{\left(x-y\right)\left(-xy-x^2-xy-y^2\right)}\)
\(=\dfrac{\left(x-y\right)^2\cdot\left(x+y\right)^2}{xy\left(-x^2-2xy-y^2\right)}\)
\(=\dfrac{\left(x-y\right)^2\cdot\left(x+y\right)^2}{-xy\left(x+y\right)^2}=\dfrac{-\left(x-y\right)^2}{xy}\)
