If $x + \frac{1}{x} = 6$, what is the value of $\frac{x^2 - x + 1}{x^2 + x + 1}$?
Options:
- A: $\frac{3}{4}$
- B: $\frac{5}{7}$
- C: $\frac{4}{5}$
- D: $\frac{1}{2}$
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