Unfamiliar.

Is it true that the minimum value of

$\large \displaystyle A = \dfrac{(2y + 2z - x)x^3 + (2z + 2x - y)y^3 + (2x + 2y - z)z^3 - 3(x + y + z)xyz}{x^3 + y^3 + z^3 - 3xyz}$

is 3 with $x, y, z \in \mathbb R$ and $\displaystyle \dfrac{yz + zx + xy}{x + y + z} \ne 0$ ?

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Bonus

• If the answer is true, prove why.

• If the answer is false, calculate the minimum value of $A$ (if possible).