To solve the expression \(-\frac{12}{7} + \frac{3}{14}\), we need to find a common denominator.
The denominators are 7 and 14. The least common denominator (LCD) is 14. We will convert \(-\frac{12}{7}\) to a fraction with a denominator of 14.
To convert \(-\frac{12}{7}\): \[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \]
Now we can rewrite the expression: \[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
Now we will reduce \(\frac{-21}{14}\). The greatest common divisor (GCD) of 21 and 14 is 7. We simplify: \[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]
Thus, the final answer is: \[ \boxed{-\frac{3}{2}} \]
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