Question

Rút gọn biểu thức:

A= \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}+\frac{x-y}{\sqrt{x}-\sqrt{y}}\) (với x, y > 0; x ≠ y)

Answer 1

\(A=\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}+\frac{x-y}{\sqrt{x}-\sqrt{y}}\)

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

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

\(A=\sqrt{x}-\sqrt{y}+\sqrt{x}+\sqrt{y}\)

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