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What is the minimum value of the $$ \frac {x^2 + x + 1 } {x^2 - x + 1 } \ ?$$

I have solved by equating it to m and then discriminant greater than or equal to zero and got the answer, but can algebraic manipulation is possible

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    You can find the minimum value of a function by setting the derivative of the function to zero and solving the resulting expression for $x$.2012-07-25
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    Also, you can simplify slightly by noting that $\frac {x^2 + x + 1 } {x^2 - x + 1 } = 1+\frac {2x } {x^2 - x + 1 }$.2012-07-25
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    @Daryl: The question is labeled [algebra-precalculus], which would seem to mean we should check for non-calculus solutions.2012-07-25

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