`A=(2011×2011+1)/(2012×2011-2011)`
`=(2011×2011+1)/(2011×(2012-1))`
`=(2011×2011+1)/(2011×2011)`
`=(2011×2011)/(2011×2011)+1/(2011×2011)`
`=1+1/(2011×2011)`
`B=(2012)/(2011)`
`=(2011+1)/(2011)`
`=(2011)/(2011)+1/2011`
`=1+1/2011`
Ta có: `1/(2011×2011)<1/2011`
`⇒1+1/(2011×2011)<1+1/2011`
`⇒A<B`
Vậy $A<B$.