Question

Answer 1

a: \(B=\left(\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)^2}\right)\cdot\dfrac{\left(\sqrt{x}+1\right)^2}{3\sqrt{x}-1}\)

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

\(=\dfrac{x+\sqrt{x}-x+2\sqrt{x}-1}{\sqrt{x}-1}\cdot\dfrac{1}{3\sqrt{x}-1}=\dfrac{1}{\sqrt{x}-1}\)

b: Để \(B=\dfrac{\sqrt{x}}{2}\) thì \(\sqrt{x}\left(\sqrt{x}-1\right)=2\)

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

=>x=4