Question

[Nguyễn Hoàng Linh]

Giúp mình câu a, b bài 3 thôi ạ. 

Answer 1

[Nguyễn Lê Phước Thịnh]

Bài 3: 

a: Ta có: \(P=\left(\dfrac{2}{\sqrt{x}+2}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{x}{x\sqrt{x}-\sqrt{x}}\)

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

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

Answer 2

[Hồng Phúc]

3.

b, ĐK: \(x>0;x\ne1\)

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

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

\(\Leftrightarrow3>0\)

\(\Rightarrow P< 1\forall x>0;x\ne1\)