To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{14}\), we need a common denominator. The least common multiple of 7 and 14 is 14.
First, we rewrite \(-\frac{12}{7}\) with a denominator of 14:
\[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \]
Now, we can add the two fractions:
\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
Next, we simplify the fraction \(\frac{-21}{14}\):
Both the numerator and the denominator can be divided by their greatest common divisor, which is 7:
\[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]
Therefore, the result of \(-\frac{12}{7} + \frac{3}{14}\) as a reduced improper fraction is:
\[ \boxed{-\frac{3}{2}} \]