Question

rút gọn biểu thức:

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

Answer 1

\(\frac{x+\sqrt{x}}{\sqrt{x}}-\frac{x-4}{\sqrt{x}+2}\) (*)

điều kiện xác định: \(x\ge0\)

(*) = \(\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}}-\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\)

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

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

Answer 2

ĐKXĐ: \(x>0\)

\(=\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}}-\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\)

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

\(=3\)