Sout $(a, b, c) \in \mathbb{R}^{3}$ tel que $(a-b)(b-c)(c-a) \neq 0$. Calculer \[ A=\frac{a^{3}}{(a-b)(a-c)}+\frac{b^{3}}{(b-c)(b-a)}+\frac{c^{3}}{(c-a)(c-b)} \] Le résultat ne devra plus comporter de dénomirateur!

Step 1 ：Factorize the numerator and denominator of each term in the given expression A = a**3/((a - b)*(a - c)) + b**3/((-a + b)*(b - c)) + c**3/((-a + c)*(-b + c)).

Step 2 ：Simplify the expression by cancelling out common factors in the numerator and denominator.

Step 3 ：Combine like terms to further simplify the expression.

Step 4 ：The expression simplifies to a + b + c.

Step 5 ：Final Answer: \(\boxed{a + b + c}\)