Rút gọn biểu thức M= (x+căn y+ căn (xy)-1/(căn x +1)( căn x - căn y)

* Hướng dẫn giải

$M=\left(\frac{x+\sqrt{y}+\sqrt{xy}-1}{\sqrt{x}+1}+1\right).\left(\sqrt{x}-\sqrt{y}\right)$$=\frac{x+\sqrt{y}+\sqrt{xy}-1+\sqrt{x}+1}{\sqrt{x}+1}.\left(\sqrt{x}-\sqrt{y}\right)=\frac{x+\sqrt{y}+\sqrt{xy}+\sqrt{x}}{\sqrt{x}+1}.\left(\sqrt{x}-\sqrt{y}\right)$$=\frac{\left(x+\sqrt{xy}\right)+\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+1}.\left(\sqrt{x}-\sqrt{y}\right)=\frac{\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+1}.\left(\sqrt{x}-\sqrt{y}\right)$$=\frac{\left(\sqrt{x}+1\right).\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+1}.\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right).\left(\sqrt{x}-\sqrt{y}\right)=x-y$