kill(all)$

van=facebook.com/LearningCalculus$

f(c):=(c+1/c+1)*(c+1/c) =1;

g(c):=(3*c^100+2/c^100+1)*(c^100+2/c^100+3);

g(a);

h(c):=fullratsimp(f(c))$ h(c);

L:solve(%,c)$

create_list(rhs(L[i]),i,1,4);

first(unique(create_list(fullratsimp(g(L[i])),i,1,4)));