a: ĐKXĐ: x>=0; y>=0; y<>1;
\(P=\frac{x}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)}-\frac{y}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}+1\right)}-\frac{xy}{\left(\sqrt{x}+1\right)\left(1-\sqrt{y}\right)}\)
\(=\frac{x\left(\sqrt{x}+1\right)-y\left(1-\sqrt{y}\right)-xy\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{x\sqrt{x}+y\cdot\sqrt{y}+x-y-xy\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)\left(\sqrt{x}+1\right)}=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)+\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-xy\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}-xy\right)}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}-xy\right)}{\left(1-\sqrt{y}\right)\left(\sqrt{x}+1\right)}=\frac{\sqrt{x}\left(\sqrt{x}+1\right)-\sqrt{y}\left(\sqrt{x}+1\right)+y\left(1-x\right)}{\left(1-\sqrt{y}\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-\sqrt{y}\right)+y\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}{\left(\sqrt{x}+1\right)\left(1-\sqrt{y}\right)}=\frac{\sqrt{x}-\sqrt{y}+y\left(1-\sqrt{x}\right)}{1-\sqrt{y}}\)
\(=\frac{\sqrt{x}-y\cdot\sqrt{x}+y-\sqrt{y}}{1-\sqrt{y}}=\frac{\sqrt{x}\left(1-y\right)+\sqrt{y}\left(\sqrt{y}-1\right)}{1-\sqrt{y}}\)
\(=\frac{-\sqrt{x}\left(\sqrt{y}-1\right)\left(\sqrt{y}+1\right)+\sqrt{y}\left(\sqrt{y}-1\right)}{-\left(\sqrt{y}-1\right)}=\sqrt{x}\left(\sqrt{y}+1\right)-\sqrt{y}\)
