If `x = 2, y = 3 and z = 6`, then find the value of `(3sqrtx)/(sqrty + sqrtz) - (4 sqrty)/(sqrtz + sqrtx) + (sqrtz)/(sqrtx + sqrty)`

Explanation

`(3 sqrtx)/(sqrty + sqrtz) - (4 sqrty)/(sqrtz + sqrtx) + (sqrtz)/(sqrtx + sqrty)`
`= (3 sqrtx (sqrty - sqrtz))/((sqrty + sqrtz) (sqrty - sqrtz)) - (4 sqrty (sqrtz - sqrtx))/((sqrtz + sqrtx) (sqrtz - sqrtx)) + (sqrtz (sqrtx - sqrty))/((sqrtx + sqrty) (sqrtx - sqrty))`
`= (3 sqrtx (sqrty - sqrtz))/(y - z) - (4 sqrty (sqrtz - sqrtx))/(z -x) + (sqrtz (sqrtx - sqrty))/(x -y)`
`= (3 sqrt2 (sqrt3 - sqrt6))/(3 -6) - (4 sqrt3 (sqrt6 - sqrt2))/(6 -2) + (sqrt6 (sqrt2 - sqrt3))/(2 -3)` [Putting the value of x, y and z]
`= (3 sqrt2 (sqrt3 - sqrt6))/(-3) - (4 sqrt3 (sqrt6 - sqrt2))/(4) + (sqrt6 (sqrt2 - sqrt3))/(-1)`
`= -sqrt2 (sqrt3 - sqrt6) - sqrt3 (sqrt6 - sqrt2) - sqrt6(sqrt2 - sqrt3)`
`= -sqrt6 + sqrt12 - sqrt18 + sqrt6 - sqrt12 + sqrt18`
= 0
Hence the given expression = 0