1/\(\Leftrightarrow P=\frac{2}{x}-\left(\frac{x^2y}{xy\left(x+y\right)}+\frac{\left(y^2-x^2\right)\left(x+y\right)}{xy\left(x+y\right)}-\frac{xy^2}{xy\left(x+y\right)}\right).\frac{x+y}{x^2+xy+y^2}\)
\(\Leftrightarrow P=\frac{2}{x}-\frac{x^2y+xy^2+y^3-x^3-x^2y-xy^2}{xy\left(x+y\right)}.\frac{x+y}{x^2+xy+y^2}\)
\(\Leftrightarrow P=\frac{2}{x}-\frac{\left(y-x\right)\left(x^2+xy+y^2\right)}{xy\left(x+y\right)}.\frac{x+y}{x^2+xy+y^2}\)
\(\Leftrightarrow P=\frac{2y}{xy}-\frac{y-x}{xy}\)
\(\Leftrightarrow P=\frac{x+y}{xy}\)