a) \(P=\left(\frac{x+3}{x-9}+\frac{1}{\sqrt{x}+3}\right):\frac{\sqrt{x}}{\sqrt{x}-3}\)
\(P=\left(\frac{x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\frac{\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right)\cdot\frac{\sqrt{x}-3}{\sqrt{x}}\)
\(P=\frac{x+3+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\frac{\sqrt{x}-3}{\sqrt{x}}\)
\(P=\frac{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\cdot\sqrt{x}}\)
\(P=\frac{\sqrt{x}+1}{\sqrt{x}+3}\)
b) Xét \(\frac{1}{3}\)có \(1< 3\)và \(\sqrt{x}\ge0\)
\(\Rightarrow\frac{1}{3}< \frac{1+\sqrt{x}}{3+\sqrt{x}}=P\)
