`({\sqrt{x}}/{2\sqrt{x}-2}-{\sqrt{x}}/{2\sqrt{x}+2}): {\sqrt{x}}/{x+2\sqrt{x}+1}` $(x>0; x\ne 1)$
`=[{\sqrt{x}}/{2(\sqrt{x}-1)}-{\sqrt{x}}/{2(\sqrt{x}+1)}] : {\sqrt{x}}/{(\sqrt{x}+1)^2}`
`=[{\sqrt{x}(\sqrt{x}+1)-\sqrt{x}.(\sqrt{x}-1)}/{2(\sqrt{x}-1)(\sqrt{x}+1)}] . {(\sqrt{x}+1)^2}/{\sqrt{x}}`
`={x+\sqrt{x}-x+\sqrt{x}}/{2(\sqrt{x}-1)(\sqrt{x}+1)} . {(\sqrt{x}+1)^2}/{\sqrt{x}}`
`={2\sqrt{x}.(\sqrt{x}+1)}/{2.(\sqrt{x}-1).\sqrt{x}}`
`={\sqrt{x}+1}/{\sqrt{x}-1}`
