Question

Rút gọn D

Với x> 0 và x khác 1

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

Answer 1

\(D=\frac{1}{x-\sqrt{x}}-\frac{2\sqrt{x}}{x-1}+\frac{1}{x+\sqrt{x}}\left(ĐK:x>0;x\ne1\right)\)

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

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