$P=\frac{x\sqrt{x}-3}{(\sqrt{x}-3)(\sqrt{x}+1)}-\frac{2(\sqrt{x}-3)^2}{(\sqrt{x}-3)(\sqrt{x}+1)}-\frac{(\sqrt{x}+3)(\sqrt{x}+1)}{(\sqrt{x}-3)(\sqrt{x}+1)}$$=\frac{x\sqrt{x}-3x+8\sqrt{x}-24}{(\sqrt{x}-3)(\sqrt{x}+1)}$
$=\frac{(\sqrt{x}-3)(x+8)}{(\sqrt{x}-3)(\sqrt{x}+1)}=\frac{x+8}{\sqrt{x}+1}=\sqrt{x}+1+\frac{9}{\sqrt{x}+1}-2\geq 4$