Haha thats allright.
Since you have x as a fraction, x = a/b, 1/x just equals the reciprocal, which is b/a.
So if x = 3 - 2sqrt(2) / 3 + 2sqrt(2)
x + 1/x = [ (3 - 2sqrt2) / (3 + 2sqrt2) ] + [ (3 + 2sqrt2) / (3 - 2sqrt2) ]
= [(3-2sqrt2)^2 + (3 + 2sqrt2)^2 ] / [ (3 + 2sqrt2)(3 - 2sqrt2) ]
= [ 9...