Question

Rút gọn biểu thức A=\(\left(\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\right):\dfrac{\sqrt{xy}}{x-y}\)

Answer 1

\(A=\left(\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\right):\dfrac{\sqrt{xy}}{x-y}\)

\(A=\dfrac{\left(\sqrt{x}+\sqrt{y}\right)^2-\left(\sqrt{x}-\sqrt{y}\right)^2}{x-y}:\dfrac{\sqrt{xy}}{x-y}\)

\(A=\dfrac{x+2\sqrt{xy}+y-x+2\sqrt{xy}-y}{\sqrt{xy}}=\dfrac{4\sqrt{xy}}{\sqrt{xy}}=4\)

Answer 2

\(A=\left(\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\right):\dfrac{\sqrt{xy}}{x-y}\)

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

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

\(=\dfrac{2\sqrt{x}\cdot2\sqrt{y}}{x-y}\cdot\dfrac{x-y}{\sqrt{xy}}\)

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

\(=4\)