Question

P=\(\left(\frac{x+3\sqrt{x}+2}{x\sqrt{x}-8}-\frac{1}{\sqrt{x}-2}\right):\frac{1}{\sqrt{x}}\)

Answer 1

Ta có: \(P=\left(\frac{x+3\sqrt{x}+2}{x\sqrt{x}-8}-\frac{1}{\sqrt{x}-2}\right):\frac{1}{\sqrt{x}}\)

\(=\left(\frac{x+3\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+4\right)}-\frac{x+2\sqrt{x}+4}{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+4\right)}\right)\cdot\sqrt{x}\)

\(=\frac{x+3\sqrt{x}+2-x-2\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+4\right)}\cdot\sqrt{x}\)

\(=\frac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+4\right)}\cdot\sqrt{x}\)

\(=\frac{\sqrt{x}}{x+2\sqrt{x}+4}\)