# Don't use calculus

Algebra Level 3

$\large \frac{(x+\frac{1}{x})^{6}-(x^{6}+\frac{1}{x^{6}})-2}{(x+\frac{1}{x})^{3}+(x^{3}+\frac{1}{x^{3}})}$

Find the minimum value of the expression above for positive $x$.

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