Question

[Nguyễn Thị Diệu Nhi]

Rút gọn 

(x căn y + y căn x) (căn x - căn y) / căn xy

Answer 1

[Lê Tài Bảo Châu]

Em làm thử thoi

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

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

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

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

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

\(=x-y\)