$\begin{array}{l}
P = (1 - \frac{{\sqrt x }}{{\sqrt x + 1}}):(\frac{{\sqrt x + 3}}{{\sqrt x - 2}} + \frac{{\sqrt x + 2}}{{3 - \sqrt x }} + \frac{{\sqrt x + 2}}{{(\sqrt x - 2)(\sqrt x - 3)}})(x \ge 0,x \ne 4,x \ne 9)\\
= (\frac{{\sqrt x + 1 - \sqrt x }}{{\sqrt x + 1}}):(\frac{{(\sqrt x + 3)(\sqrt x - 3) + (\sqrt x + 2)( - \sqrt x + 2) + \sqrt x + 2}}{{(\sqrt x - 2)(\sqrt x - 3)}})\\
= \frac{1}{{\sqrt x + 1}}:(\frac{{x - 9 + 4 - x + \sqrt x + 2}}{{(\sqrt x - 2)(\sqrt x - 3)}}) = \frac{1}{{\sqrt x + 1}}:\frac{{\sqrt x - 3}}{{(\sqrt x - 2)(\sqrt x - 3)}} = \frac{{(\sqrt x - 2)}}{{(\sqrt x + 1)}}\\
P < 0 \to \frac{{(\sqrt x - 2)}}{{(\sqrt x + 1)}} < 0 \to (\sqrt x - 2) < 0 \to x < 4\\
\to 0 \le x < 4
\end{array}$
