To add \(-\frac{12}{7}\) and \(\frac{3}{14}\), we first need to have a common denominator.
The denominators are 7 and 14. The least common denominator (LCD) is 14.
Now we can 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:
\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
We can simplify \(\frac{-21}{14}\):
\[ \frac{-21}{14} = \frac{-3}{2} \quad \text{(by dividing the numerator and denominator by 7)} \]
Therefore,
\[ -\frac{12}{7} + \frac{3}{14} = -\frac{3}{2} \]