`1/{1.2} + 1/{2.3} + 1/{3.4} + .... + 1/{x.(x+1)} = 2008/2009`
`⇔ 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/x - 1/{x+1} = 2008/2009`
`⇔ 1 - 1/{x+1} = 2008/2009`
`⇔ 1/{x+1} = 1/2009`
`⇔ x + 1 = 2009`
`⇔ x = 2008`
Vậy `x=2008`
`(2/{11.13} + 2/{13.15} + .... + 2/{19.21} ) - x + 23/231 = 5/77`
`⇔ (2/11 - 2/13 + 2/13 - 2/15 + .... + 2/19 - 2/21) - x = -8/231`
`⇔ (1/11 - 1/21) - x = -8/231`
`⇔ x = 6/77`
Vậy `x=6/77`
