Question

Answer 1

1: Ta có: \(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\)

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

\(=\frac{4+4\sqrt{x}+x-4+4\sqrt{x}-x+4x}{4-x}=\frac{4x+8\sqrt{x}}{4-x}=\frac{4\sqrt{x}\left(\sqrt{x}+2\right)}{-\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}=-\frac{4\sqrt{x}}{\sqrt{x}-2}\)

Ta có: \(P=\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right):\frac{\sqrt{x}-3}{2\sqrt{x}-x}\)

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