Question

rút gọn biểu thức:

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

Answer 1

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

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

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

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

\(=\dfrac{2x}{x-4}\cdot\dfrac{x-4}{2\sqrt{x}}\)

\(=\sqrt{x}\)