Question

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

a) Rút gọn A

b) Tìm x để A=\(\dfrac{4}{\sqrt{x}+4}\)

 

Answer 1

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

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

b: Để A=4/(căn x+4) thì \(\dfrac{2}{x-1}=\dfrac{4}{\sqrt{x}+1}=\dfrac{4\left(\sqrt{x}-1\right)}{x-1}\)

=>4 căn x-4=2

=>4 căn x=6

=>x=9/4