Three charged particles line on an $x$ axis, as shown in Fig. $1.$ Particles $1$ and $2$ are fixed in place. Particle $3$ is free to move, but the net electrostatic force on it from particles $1$ and $2$ happens to be zero at this point. If $L_{23}=3L_{12},$ what is the ratio of $\frac{q_1}{q_2}?$