Question

Answer 1

a: ĐKXĐ: \(\left\{{}\begin{matrix}x>0\\x\ne9\end{matrix}\right.\)

\(P=\left(\dfrac{x+3}{x-9}+\dfrac{1}{\sqrt{x}+3}\right):\dfrac{\sqrt{x}}{\sqrt{x}-3}\)

\(=\dfrac{x+3+\sqrt{x}-3}{x-9}\cdot\dfrac{\sqrt{x}-3}{\sqrt[]{x}}\)

\(=\dfrac{x+\sqrt{x}}{\sqrt{x}+3}\cdot\dfrac{1}{\sqrt{x}}=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\)

b: \(P-\dfrac{1}{3}=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}-\dfrac{1}{3}\)

\(=\dfrac{3\left(\sqrt{x}+1\right)-\sqrt{x}-3}{3\left(\sqrt{x}+3\right)}=\dfrac{2\sqrt{x}}{3\left(\sqrt{x}+3\right)}>0\)

=>\(P>\dfrac{1}{3}\)