7. Given complex numbers $Z_{1}, Z_{2}$ satisfy $\left|Z_{1}\right|=2,\left|Z_{2}\right|=3$. If the angle between the vectors they correspond to is $60^{\circ}$, then $\left|\frac{Z_{1}+Z_{2}}{Z_{1}-Z_{2}}\right|=$ $\qquad$ .
7. $\frac{\sqrt{133}}{7}$

As shown in the figure, by the cosine rule we get:
$$
\left|Z_{1}+Z_{2}\right|=\sqrt{19},\left|Z_{1}-Z_{2}\right|=\sqrt{7} \text {, }
$$

Therefore,
$$
\left|\frac{Z_{1}+Z_{2}}{Z_{1}-Z_{2}}\right|=\frac{\sqrt{19}}{\sqrt{7}}=\frac{\sqrt{133}}{7} .
$$