kill(all)$

van=facbeook.com/LearningCalculus$

f(a,b,c):=(a^3*(b^2-c^2) + b^3*(c^2-a^2) + c^3*(a^2-b^2))/
          (a^2*(b^1-c^1) + b^2*(c^1-a^1) + c^2*(a^1-b^1))$

fullratsimp(f(a,b,c));