Question

cho biểu thức Q=(\(\frac{\sqrt{x}}{\sqrt{x}-1}\)-\(\frac{\sqrt{x}}{x-\sqrt{x}}\)):\(\frac{\sqrt{x}+1}{x-1}\)với x>0,x≠1

a) Rút gọn Q

b)tìm x để Q>0

Answer 1

https://i.imgur.com/m78fdp1.jpg

Answer 2

<=> \((\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{\sqrt{x}}{\sqrt{x}(\sqrt{x}-1)}).\frac{x-1}{\sqrt{x}+1}\)

<=> \(\frac{x-\sqrt{x}}{\sqrt{x}(\sqrt{x}-1)}.\frac{x-1}{\sqrt{x}+1}\)

<=> \(\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}.\frac{x-1}{\sqrt{x}+1}\)

<=>\(\frac{x-1}{\sqrt{x}+1}\Leftrightarrow\sqrt{x}-1\)

Để Q >0 thì \(\sqrt{x}-1>0\)

\(\sqrt{x}>1\Leftrightarrow x>1\)

Vậy để Q>o thì x>1