Question

Cho biểu thức P=\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right)\times\left(\dfrac{1}{2\sqrt{x}}-\dfrac{\sqrt{x}}{2}\right)^2\)

a Rút gọn P

b Tìm x để \(\dfrac{P}{\sqrt{x}}>2\)

Answer 1

Answer 2

a: \(=\dfrac{x-2\sqrt{x}+1-x-2\sqrt{x}-1}{x-1}\cdot\left(\dfrac{1-x}{2\sqrt{x}}\right)^2\)

\(=\dfrac{-4\sqrt{x}}{x-1}\cdot\dfrac{\left(x-1\right)^2}{4x}=\dfrac{-\left(x-1\right)}{\sqrt{x}}\)

b: \(\dfrac{P}{\sqrt{x}}>2\)

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

=>\(\dfrac{-x+1}{x}-2>0\)

=>\(\dfrac{-x+1-2x}{x}>0\)

\(\Leftrightarrow\dfrac{3x-1}{x}< 0\)

=>0<x<1/3