Question

\(A=\left(\frac{1}{x+\sqrt{x}}-\frac{1}{\sqrt{x}+1}\right)\div\frac{\sqrt{x}-1}{x+2\sqrt{x}+1}\left(x>0,x\ne1\right)\)

Rút Gọn

Answer 1

\(A=\left[\frac{1}{\sqrt{x}\left(\sqrt{x}+1\right)}-\frac{1}{\sqrt{x}+1}\right]\div\frac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)^2}\)

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

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

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