kill(all)$

van=facebook.com/LearningCalculus$

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

fullratsimp(1/f(a,b,c))$

g(a,b,c):=''(factor(fullratsimp(1/f(a,b,c))));

g(389,508,1826);

float(%);