Question

C/m:

\(\dfrac{x+2}{x\sqrt{x}+1}+\dfrac{\sqrt{x}-1}{x-\sqrt{x}+1}-\dfrac{\sqrt{x-1}}{x-1}< 1\)

Answer 1

Dễ thế mà ko bt làm

Answer 2

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

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

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

\(A-1=\dfrac{\sqrt{x}-x+\sqrt{x}-1}{x-\sqrt{x}+1}=\dfrac{-\left(\sqrt{x}-1\right)^2}{x-\sqrt{x}+1}< 0\)

=>A<1