Simplify: `(1)/(sqrt2 +1) + (1)/(sqrt3 + sqrt2) + (1)/(sqrt4 + sqrt3)`

Explanation

`(1)/(sqrt2 + 1) + (1)/(sqrt3 + sqrt2) +(1)/(sqrt4 + sqrt3)`
`(1)/(sqrt2 +1) xx (sqrt2 -1)/(sqrt2 -1) + (1)/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) + (1)/(sqrt4 + sqrt3) xx (sqrt4 - sqrt3)/(sqrt4 - sqrt3)`
`= (sqrt2-1)/((sqrt2)^(2) - (1)^(2)) + (sqrt3 - sqrt2)/((sqrt3)^(2) - (sqrt2)^(2)) + (sqrt4- sqrt3)/((sqrt4)^(2) - (sqrt3)^(2))`
`= (sqrt2 -1)/(2-1) + (sqrt3 - sqrt2)/(3-2) + (sqrt4 - sqrt3)/(4-3)`
`= sqrt2 -1 + sqrt3 -sqrt2 + sqrt4 - sqrt3 = -1 + sqrt4 = -1 + 2 =1`
Hence the required simplified value = 1