Question

[Duong Thi Nhuong]

Rút gọn D =   \(\left(\frac{\sqrt{x}+\sqrt{y}}{2\sqrt{x}-2\sqrt{y}}-\frac{2\sqrt{x}}{x-y}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

Sửa đề; \(D=\left(\dfrac{\sqrt{x}+\sqrt{y}}{2\sqrt{x}-2\sqrt{y}}-\dfrac{2\sqrt{xy}}{x-y}\right)\cdot\dfrac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

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

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