Rút gọn \(P=\left(\frac{\sqrt{x}+\sqrt{y}}{1-\sqrt{x y}}+\frac{\sqrt{x}-\sqrt{y}}{1+\sqrt{x y}}\right):\left(1+\frac{x+y+2 x y}{1-x y}\right)\) ta được

* Hướng dẫn giải

\(Đ K X Đ: x \geq 0 ; y \geq 0 ; x y \neq 1\)

Khi đó ta có

\(\begin{aligned} P &=\frac{(\sqrt{x}+\sqrt{y})(1+\sqrt{x y})+(\sqrt{x}-\sqrt{y})(1-\sqrt{x y})}{1-x y}: \frac{1-x y+x+y+2 x y}{1-x y} \\ &=\frac{\sqrt{x}+x \sqrt{y}+\sqrt{y}+y \sqrt{x}+\sqrt{x}-x \sqrt{y}-\sqrt{y}+y \sqrt{x}}{1-x y} \cdot \frac{1-x y}{1+x+y+x y} \\ &=\frac{2(\sqrt{x}+y \sqrt{x})}{(1+x)(1+y)}=\frac{2 \sqrt{x}(1+y)}{(1+x)(1+y)}=\frac{2 \sqrt{x}}{1+x} \end{aligned}\)