a: \(P=\left(\dfrac{x+2}{x\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\right)\cdot\dfrac{4\sqrt{x}}{3}\)
\(=\left(\dfrac{x+2}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}-\dfrac{1}{\sqrt{x}+1}\right)\cdot\dfrac{4\sqrt{x}}{3}\)
\(=\dfrac{x+2-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\cdot\dfrac{4\sqrt{x}}{3}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+1}\cdot\dfrac{4\sqrt{x}}{3\left(x-\sqrt{x}+1\right)}=\dfrac{4}{3}\cdot\dfrac{\sqrt{x}}{x-\sqrt{x}+1}\)
b: P=8/9
=>\(\dfrac{\sqrt{x}}{x-\sqrt{x}+1}=\dfrac{8}{9}:\dfrac{4}{3}=\dfrac{8}{9}\cdot\dfrac{3}{4}=\dfrac{2}{3}\)
=>\(2x-2\sqrt{x}+2=3\sqrt{x}\)
=>\(2x-5\sqrt{x}+2=0\)
=>\(\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)=0\)
=>x=1/4 hoặc x=4
