Question

Cho bthuc

A=\(\left(\dfrac{\sqrt{2}-2}{\sqrt{x}+2}-\dfrac{8\sqrt{x}}{4-x}\right):\dfrac{\sqrt{x}+2}{1-2\sqrt{x}}\) với \(x\ge0,x\ne4\)

a,Rút gọn

b,Tìm x để A=\(-\dfrac{1}{3}\)

Answer 1

a: \(A=\left(\dfrac{\sqrt{x}-2}{\sqrt{x}+2}+\dfrac{8\sqrt{x}}{x-4}\right):\dfrac{\sqrt{x}+2}{1-2\sqrt{x}}\)

\(=\dfrac{x-4\sqrt{x}+4+8\sqrt{x}}{x-4}:\dfrac{\sqrt{x}+2}{1-2\sqrt{x}}\)

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

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

b: Để A=-1/3 thì \(\dfrac{2\sqrt{x}-1}{\sqrt{x}-2}=\dfrac{1}{3}\)

=>6 căn x-3=căn x-2

=>5 căn x=1

hay x=1/25