`((x+2\sqrt{x})/(x-2\sqrt{x})+(\sqrt{x})/(\sqrt{x}-2))*1/(\sqrt{x}+1)`
`=[(\sqrt{x}(\sqrt{x}+2))/(\sqrt{x}(\sqrt{x}-2))+(\sqrt{x})/(\sqrt{x}-2))*1/(\sqrt{x}+1)`
`=((\sqrt{x}+2)/(\sqrt{x}-2)+(\sqrt{x})/(\sqrt{x}-2))*1/(\sqrt{x}+1)`
`=(\sqrt{x}+2+\sqrt{x})/(\sqrt{x}-2)*1/(\sqrt{x}+1)`
`=(2\sqrt{x}+2)/(\sqrt{x}-2)*1/(\sqrt{x}+1)`
`=(2(\sqrt{x}+1))/(\sqrt{x}-2)*1/(\sqrt{x}+1)`
`=2/(\sqrt{x}-2)`
