Question

P = \(\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right):\frac{\sqrt{x}-3}{2\sqrt{x}-x}\)

Tính x để P > 0 và P < 0

Answer 1

\(=\left(\dfrac{-\left(\sqrt{x}+2\right)}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+2}-\dfrac{4x}{x-4}\right)\cdot\dfrac{2\sqrt{x}-x}{\sqrt{x}-3}\)

\(=\dfrac{-x-4\sqrt{x}-4+x-4\sqrt{x}+4-4x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{-\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}-3}\)

\(=\dfrac{-4x-8\sqrt{x}}{\sqrt{x}+2}\cdot\dfrac{-\sqrt{x}}{\sqrt{x}-3}\)

\(=\dfrac{4x}{\sqrt{x}-3}\)

Để P>0 thì \(\sqrt{x}-3>0\)

hay x>9

Để P<0 thì \(\sqrt{x}-3< 0\)

hay 0<x<9