kill(all)$

van=facebook.com/LearningCalculus$

f(x):=3*b*x^2-4*a*x+3*b;

A:(sqrt(2*a+3*b)+sqrt(2*a-3*b));
B:(sqrt(2*a+3*b)-sqrt(2*a-3*b));

f(A/B)=0;

fullratsimp(%);