Question

(1/√x + 2- 1/2-√x):√x/x-4(Với x>0;x khác 0)

Answer 1

ĐKXĐ: x>0; x<>4

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

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

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

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