[tex]P = (\frac{x\sqrt{x} - y\sqrt{y}}{\sqrt{x} - \sqrt{y}} + \sqrt{xy}).(\frac{\sqrt{x} - \sqrt{y}}{x - y})^{2}
\Leftrightarrow P = [\frac{(x + \sqrt{xy} + y)(\sqrt{x} - \sqrt{y})}{\sqrt{x} - \sqrt{y}} + \sqrt{xy}][\frac{\sqrt{x} - \sqrt{y}}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})}]^{2}
\Leftrightarrow P = (x + 2\sqrt{xy} + y).\frac{1}{(\sqrt{x} + \sqrt{y})^{2}}
\Leftrightarrow P = \frac{(\sqrt{x} + \sqrt{y})^{2}}{(\sqrt{x} + \sqrt{y})^{2}}
\Leftrightarrow P = 1[/tex]