MN ơi giúp mình với huhu
1: \(\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}+\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{1-\sqrt{xy}}+1\)
\(=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{xy}-1\right)-\sqrt{x}\left(\sqrt{y}+1\right)\left(\sqrt{xy}+1\right)+xy-1}{xy-1}\)
\(=\dfrac{x\sqrt{y}-\sqrt{x}+\sqrt{xy}-1-\left(\sqrt{xy}+\sqrt{x}\right)\left(\sqrt{xy}+1\right)+xy-1}{xy-1}\)
\(=\dfrac{x\sqrt{y}-\sqrt{x}+\sqrt{xy}+xy-2-xy-\sqrt{xy}-x\sqrt{y}-\sqrt{x}}{xy-1}\)
\(=\dfrac{-2\sqrt{x}-2}{xy-1}\)
\(1-\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}-\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{\sqrt{xy}-1}\)
\(=\dfrac{xy-1-\left(\sqrt{x}+1\right)\left(\sqrt{xy}-1\right)-\left(\sqrt{xy}+\sqrt{x}\right)\left(\sqrt{xy}+1\right)}{xy-1}\)
\(=\dfrac{xy-1-x\sqrt{y}+\sqrt{x}-\sqrt{xy}+1-xy-\sqrt{xy}-x\sqrt{y}-\sqrt{x}}{xy-1}\)
\(=\dfrac{-2x\sqrt{y}-2\sqrt{xy}}{xy-1}\)
\(R=\left(\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}+\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{1-\sqrt{xy}}+1\right):\left(1-\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}-\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{\sqrt{xy}-1}\right)\)
\(=\dfrac{-2\cdot\left(\sqrt{x}-1\right)}{xy-1}:\dfrac{-2\sqrt{xy}\left(\sqrt{x}+1\right)}{xy-1}\)
\(=\dfrac{-2\left(\sqrt{x}-1\right)}{-2\sqrt{xy}\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{xy}\left(\sqrt{x}+1\right)}\)
2: Thay \(x=2\left(3-\sqrt{5}\right)=6-2\sqrt{5}=\left(\sqrt{5}-1\right)^2;y=2\left(3+\sqrt{5}\right)=\left(\sqrt{5}+1\right)^2\) \(R=\dfrac{\sqrt{\left(\sqrt{5}-1\right)^2}-1}{\sqrt{\left(\sqrt{5}-1\right)^2\cdot\left(\sqrt{5}+1\right)^2}\left(\sqrt{\left(\sqrt{5}-1\right)^2}+1\right)}\)
\(=\dfrac{\sqrt{5}-1-1}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)\left(\sqrt{5}-1+1\right)}=\dfrac{\sqrt{5}-2}{4\sqrt{5}}=\dfrac{5-2\sqrt{5}}{20}\)
