ĐKXĐ: \(x\ge0;x\ne9\)
\(P=\frac{x\sqrt{x}-3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}-\frac{2\left(\sqrt{x}-3\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}-\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{x\sqrt{x}-3-2\left(x-6\sqrt{x}+9\right)-\left(x+4\sqrt{x}+3\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{x\sqrt{x}-3x+8\sqrt{x}-24}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}=\frac{\left(\sqrt{x}-3\right)\left(x+8\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{x+8}{\sqrt{x}+1}\)
\(x=14-6\sqrt{x}\Rightarrow x+6\sqrt{x}-14=0\Rightarrow\left[{}\begin{matrix}\sqrt{x}=\sqrt{23}-3\\\sqrt{x}=-\sqrt{23}-3< 0\left(l\right)\end{matrix}\right.\)
\(\Rightarrow P=\frac{\left(\sqrt{23}-3\right)^2+8}{\sqrt{23}-3+1}=\frac{40-6\sqrt{23}}{\sqrt{23}-2}\)
Kết quả xấu quá, chắc bạn ghi nhầm đề
\(P=\frac{x+8}{\sqrt{x}+1}=\sqrt{x}-1+\frac{9}{\sqrt{x}+1}=\sqrt{x}+1+\frac{9}{\sqrt{x}+1}-2\)
\(\Rightarrow P\ge2\sqrt{\frac{9\left(\sqrt{x}+1\right)}{\sqrt{x}+1}}-2=4\)
\(P_{min}=4\) khi \(\sqrt{x}+1=3\Rightarrow x=4\)
