Sove : `2 sqrt(x/a) + 3 sqrt(a/x) = b/a + (6a)/b`

If x = (sqrt(a + 3b) + sqrt(a - 3b))/ (sqrt(a + 3b) - sqrt(a - 3b)) prove that : 3bx^(2) - 2ax + 3b = 0 .

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

If x = (sqrt(2a + 3b)+sqrt(2a - 3b))/(sqrt(2a + 3b) - sqrt(2a - 3b)) , show that 3bx^(2) - 4ax + 3b = 0 .

if x = (sqrt(3a + 2b) + sqrt(3a - 2b))/(sqrt(3a + 2b) - sqrt(3a - 2b)) prove that : bx^(2) - 3ax + b = 0

If x = (4 sqrt(ab))/(sqrt a + sqrt b) , then what is the value of (x + 2sqrt a)/(x - 2 sqrta) + (x + 2 sqrtb)/(x - 2 sqrt b) " (when " a ne b) ?