Question

Answer 1

a: \(N=\dfrac{x+2-x+\sqrt{x}-1}{x\sqrt{x}+1}\cdot\dfrac{4\sqrt{x}}{3}\)

\(=\dfrac{\sqrt{x}+1}{x\sqrt{x}+1}\cdot\dfrac{4\sqrt{x}}{3}\)

\(=\dfrac{4\sqrt{x}}{3\left(x-\sqrt{x}+1\right)}\)

b: Để \(N=\dfrac{8}{9}\) thì \(\dfrac{4\sqrt{x}}{3\left(x-\sqrt{x}+1\right)}=\dfrac{8}{9}\)

\(\Leftrightarrow24x-24\sqrt{x}+24=36\sqrt{x}\)

\(\Leftrightarrow24x-60\sqrt{x}+24=0\)

\(\Leftrightarrow2x-5\sqrt{x}+2=0\)

\(\Leftrightarrow\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)=0\)

=>x=1/4 hoặc x=4