If `x` is real and `k=(x^2-x+1)/(x^2+x+1)` , then `k in [1//3,3]` (b) `kgeq3` (c) `klt=1//3` (d) none of these

Explanation

To solve the problem where \( k = \frac{x^2 - x + 1}{x^2 + x + 1} \) and we need to find the range of \( k \) such that \( k \in \left[\frac{1}{3}, 3\right] \), we will follow these steps:

### Step 1: Set up the equation
We start with the equation:
\[ k = \frac{x^2 - x + 1}{x^2 + x + 1} \]
We can rearrange this to eliminate the fraction:
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