van=facebook.com/LearningCalculus$

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

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