If `a =( 4sqrt(6))/(sqrt(2)+sqrt(3))` then the value of `(a+2sqrt(2))/(a-2sqrt(2))+(a+2sqrt(3))/(a-2sqrt(3))`

Answer

2

Explanation

If `x= (4sqrt(6))/(sqrt(2)+sqrt(3))` then …………
`x = (4sqrt(6))/(sqrt(2)+sqrt(3))` , `:. (x)/(2sqrt(2)) = (2sqrt(3))/(sqrt(3)+sqrt(3))`
using `C-D` rule `(x+2sqrt(2))/(x-2sqrt(2)) = (3sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))` ……… (1)
Also `(x)/(2sqrt(3)) = (2sqrt(2))/(sqrt(2)+sqrt(3))`
`implies (x+2sqrt(3))/(x-2sqrt(3)) = (3sqrt(2)+sqrt(3))/(sqrt(2)-sqrt(3))/(sqrt(2)-sqrt(3))` ........ (2)
`(x+2sqrt(2))/(x-2sqrt(2))+(x+2sqrt(3))/(x-2sqrt(3)) = 2`