Difference of cubic vieta's

Algebra Level 3

Let a,b,a,b, and cc be the roots of the equation 2x3x2+x+3=02x^{3}-x^{2}+x+3=0. Find the value of the expression below.

a3b3ab+b3c3bc+c3a3ca \large \frac{a^{3}-b^{3}}{a-b}+\frac{b^{3}-c^{3}}{b-c}+\frac{c^{3}-a^{3}}{c-a}

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