To solve the expression \(-\frac{12}{7} + \frac{3}{14}\), we first need to find a common denominator. The denominators are 7 and 14. The least common denominator (LCD) is 14.
Next, we convert \(-\frac{12}{7}\) so that it has a denominator of 14:
\[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \]
Now, we can rewrite the original expression using the common denominator:
\[ -\frac{24}{14} + \frac{3}{14} \]
Now, we can combine the fractions:
\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]
Next, we simplify \(\frac{-21}{14}\) by finding the greatest common divisor (GCD) of the numerator and the denominator. Both 21 and 14 can be divided by 7:
\[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]
Thus, the final answer in reduced improper fraction form is:
\[ \boxed{-\frac{3}{2}} \]
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