Question

cho biểu thức: P=\(\sqrt{\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+x+1}\)

Rút gọn P với \(0\le x\le1\)

Answer 1

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

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

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

  =\(\sqrt{x-2\sqrt{x}+1}\)

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

  =\(\sqrt{x}-1\)