To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{14}\), we first need a common denominator. The denominators are 7 and 14. The least common denominator (LCD) is 14.
Now we will convert \(-\frac{12}{7}\) to a fraction 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 can simplify \(\frac{-21}{14}\). Both the numerator and the denominator can be divided by 7:
\[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]
So, the final answer is:
\[ -\frac{3}{2} \]