To add the fractions \(-\frac{12}{7} + \frac{3}{14}\), we need to find a common denominator. The denominators are \(7\) and \(14\). The least common denominator (LCD) is \(14\).
Now we need to convert \(-\frac{12}{7}\) to have a denominator of \(14\):
\[ -\frac{12}{7} \times \frac{2}{2} = -\frac{24}{14} \]
Now we can add the two fractions:
\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
Next, we can simplify \(-\frac{21}{14}\). Both the numerator and the denominator can be divided by \(7\):
\[ -\frac{21 \div 7}{14 \div 7} = -\frac{3}{2} \]
Thus, the answer as a reduced improper fraction is:
\[ \boxed{-\frac{3}{2}} \]