Question

\(\left(\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{\sqrt{x}}{\sqrt{x}+2}\right).\frac{x-4}{\sqrt{4x}}\)
Tìm ĐKXĐ và rút gọn

Answer 1

dk , x  lơn hơn hoặc = 0  , x khác 4

\(\frac{\sqrt{x}}{\sqrt{x-2}}\times\frac{x-4}{2\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x+2}}\times\frac{x-4}{2\sqrt{x}}.\)

có  \(x-4=\left(\sqrt{x}-2\right)\left(\sqrt{x+2}\right)\)

\(\frac{\sqrt{x}}{\sqrt{x}-2}\times\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{2\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+2}+\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{2\sqrt{x}}\)

rút gọn 

\(\frac{\left(\sqrt{x}+2\right)}{2}+\frac{\left(\sqrt{x}-2\right)}{2}\)

\(\frac{2\sqrt{x}}{2}\)