\[\frac{x_{1}q + x_{1}q^{2} + x_{1}q^{3}}{x_{1}q^{2} + x_{1}q^{3}} =\]
\[\frac{1 + q + q^{2}}{q + q^{2}} = \frac{13}{12}\]
\[12 \cdot \left( 1 + q + q^{2} \right) = 13 \cdot \left( q + q^{2} \right)\]
\[12 + 12q + 12q^{2} = 13q + 13q^{2}\]
\[q^{2} + q - 12 = 0\]
\[q_{1} = - 4;\ \ \ q_{2} = 3\]
\[Ответ:\ - 4\ или\ 3.\]