$\displaystyle \begin{array}{{>{\displaystyle}l}} P=\frac{2\sqrt{x} -9}{\left(\sqrt{x} -3\right)\left(\sqrt{x} -2\right)} \ +\frac{2\sqrt{x} +1}{\sqrt{x} -3} -\frac{\sqrt{x} +3}{\sqrt{x} -2} \ \\ a) \ DKXD:\ \begin{cases} x\geqslant 0 & \\ \sqrt{x} \#3 & \\ \sqrt{x} \#2 & \end{cases}\rightarrow \begin{cases} x\geqslant 0 & \\ x\#9\ và\ x\#4 & \end{cases} \ \\ P=\frac{2\sqrt{x} -9+\left( 2\sqrt{x} +1\right)\left(\sqrt{x} -2\right) -\left(\sqrt{x} -3\right)\left(\sqrt{x} +3\right)}{\left(\sqrt{x} -3\right)\left(\sqrt{x} -2\right)} \ \\ P=\frac{2\sqrt{x} -9+2x-4\sqrt{x} +\sqrt{x} -2-x+9}{\left(\sqrt{x} -3\right)\left(\sqrt{x} -2\right)} \ \\ P=\frac{x-\sqrt{x} -2}{\left(\sqrt{x} -3\right)\left(\sqrt{x} -2\right)} =\frac{x-2\sqrt{x} +\sqrt{x} -2}{\left(\sqrt{x} -3\right)\left(\sqrt{x} -2\right)}\\ P=\frac{\left(\sqrt{x} +1\right)\left(\sqrt{x} -2\right)}{\left(\sqrt{x} -3\right)\left(\sqrt{x} -2\right)} =\frac{\sqrt{x} +1}{\sqrt{x} -3} \ \\ c) \ Để\ P=\frac{1}{2} \ thì\ \frac{\sqrt{x} +1}{\sqrt{x} -3} =\frac{1}{2} \ \\ \rightarrow \frac{\sqrt{x} +1}{\sqrt{x} -3} -\frac{1}{2} =0\ \\ \rightarrow \frac{2\sqrt{x} +2-\sqrt{x} +3}{2\sqrt{x} -6} =0\ \\ \rightarrow \sqrt{x} +5=0\ \\ Ta\ có\ \sqrt{x} +5\geqslant 5\ với\ mọi\ x\ \\ Do\ đó\ 0\ tồn\ tại\ x\ tm\ phương\ trình\ \\ \end{array}$
