If a + b + c = 3, then find the value of \(\frac{a^3}{a^3 + abc}\) + \(\frac{b^3}{b^3 + abc}\) + \(\frac{c^3}{c^3 + abc}\) ?

\(\frac{3}{2}\)

We have 3 variables and only one equation.

so let us put value of a = 1, b = 1 and c = 1 

\(\frac{a^3}{a^3 + abc}\) + \(\frac{b^3}{b^3 + abc}\) + \(\frac{c^3}{c^3 + abc}\) = \(\frac{1}{2}\) + \(\frac{1}{2}\)  + \(\frac{1}{2}\) = \(\frac{3}{2}\)