Let the given expression = x
So....we have that
x = 3 + 1 / x
x - 3 = 1 / x multiply through by x
x^2 - 3x = 1 complete the square on x
x^2 - 3x + 9/ 4 = 1 + 9/4
(x - 3/2)^2 = 13/4 take the positive root
x - 3/2 = √13 / 2
x = [ 3 + √13 ]
__________
2
