Question

P= \(\)

\(\left[\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}\right)\dfrac{2}{\sqrt{x}+\sqrt{y}}+\dfrac{1}{x}+\dfrac{1}{y}\right]:\dfrac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{x^3y}+\sqrt{x^3y}}\)

Tìm đk và rút gọn

Answer 1

ĐKXĐ: x>0; y>0

Sửa đề: \(P=\left[\dfrac{\sqrt{x}+\sqrt{xy}}{\sqrt{xy}}\cdot\dfrac{2}{\sqrt{x}+\sqrt{y}}+\dfrac{x+y}{xy}\right]:\dfrac{x\left(\sqrt{x}+\sqrt{y}\right)+y\left(\sqrt{y}+\sqrt{x}\right)}{\sqrt{x^3y}+\sqrt{xy^3}}\)

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