a: \(A=\dfrac{2\sqrt{x}\left(\sqrt{x}+3\right)-x-9\sqrt{x}}{x-9}=\dfrac{2x+6\sqrt{x}-x-9\sqrt{x}}{x-9}\)
\(=\dfrac{x-3\sqrt{x}}{x-9}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(B=\dfrac{\sqrt{x}\left(\sqrt{x}+5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-5}\)
b: \(P=A:B\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}+3}:\dfrac{\sqrt{x}}{\sqrt{x}-5}=\dfrac{\sqrt{x}-5}{\sqrt{x}+3}\)
c: P=2/3
=>\(\dfrac{\sqrt{x}-5}{\sqrt{x}+3}=\dfrac{2}{3}\)
=>\(3\sqrt{x}-15=2\sqrt{x}+6\)
=>căn x=21
=>x=441
d: P nhận giá trị nguyên khi \(\sqrt{x}-5⋮\sqrt{x}+3\)
=>\(\sqrt{x}+3-8⋮\sqrt{x}+3\)
=>\(\sqrt{x}+3\in\left\{4;8\right\}\)
=>x=25(loại) hoặc x=1(nhận)
e: căn x-5<căn x+3
=>\(\dfrac{\sqrt{x}-5}{\sqrt{x}+3}< 1\)
=>P<1
