Q3/024) If a=(4√6)/{(√2)+(√3)} then the value of {(a+2√2)/(a-2√2)}+{(a+2√3)/(a-2√3)… is

to keep in simple for without radicals

let x= 2√2 and y = 2√3

a=(4√6)/{(√2)+(√3)} = 2(xy)/(x + y)

so
a/x = 2y/(x+y)

using componedo dividendo (a+x)/(a-x) = ( 3y + x)/(y-x)

siminalrly (a+y)/(a-y) = ( 3x + y)/(x-y)

adding we get (a+x)/(a-x) + (a+y)/(a-y) = 2

hence {(a+2√2)/(a-2√2)}+{(a+2√3)/(a-2√3)} = 2