kill(all)$

van=facebook.com/LearningCalculus$

f(a):=''(fullratsimp((sqrt(4-a^2)*sqrt(9-a^2))/
                     (sqrt(4-a^2)+sqrt(9-a^2))-1));

f(1.23);

f(1.23118057);

incr(f,lo,hi):=
    if abs(f(lo)) < abs(f((lo+hi)/2)) then
        lo
        else if abs(f((lo+hi)/2)) < abs(f(hi)) then
            (lo+hi)/2 else hi$

incr(f,1.23118568,1.23118574);

f(%);