Question

rút gọn biểu thức
A =\(\frac{1}{\sqrt{x}+2}+\frac{\sqrt{x}}{2-\sqrt{x}}+\frac{2x-\sqrt{x}+2}{x-4}\) ( x>0, x khác 4)

Answer 1

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

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

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

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

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

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