If x2-3x + 1 = 0, the value of fraction x2 / (x ^ 4 + x2 + 1) is Ask God for help!

The denominator x ^ 4 + x ^ 2 + 1 is factorized into x ^ 4 + x ^ 2 + 1 = x ^ 4 + 2x ^ 2 + 1-x ^ 2 = (x ^ 2 + 1) ^ 2-x ^ 2 = (x ^ 2 + X + 1) (x ^ 2-x + 1), and because x ^ 2-3x + 1 = 0, x ^ 2 = 3x-1. In this way, the denominator becomes (3x-1 + X + 1) (3x-1-x + 1) = 4x · 2x = 6x ^ 2. X ^ 2 / 6x ^ 2 = 1 / 6, so the answer is 1 / 6

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