To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{-4}\), we first rewrite \(\frac{3}{-4}\) as \(-\frac{3}{4}\).
Now, our expression becomes:
\[ -\frac{12}{7} - \frac{3}{4} \]
To add these two fractions, we need a common denominator. The denominators are 7 and 4. The least common multiple (LCM) of 7 and 4 is 28.
Next, we convert each fraction to have the common denominator of 28:
- For \(-\frac{12}{7}\):
\[ -\frac{12}{7} = -\frac{12 \times 4}{7 \times 4} = -\frac{48}{28} \]
- For \(-\frac{3}{4}\):
\[ -\frac{3}{4} = -\frac{3 \times 7}{4 \times 7} = -\frac{21}{28} \]
Now we can add the two fractions:
\[ -\frac{48}{28} - \frac{21}{28} = -\frac{48 + 21}{28} = -\frac{69}{28} \]
Now we have the improper fraction \(-\frac{69}{28}\). The fraction is already in its reduced form, because 69 and 28 have no common factors other than 1.
Therefore, the final answer is:
\[ \boxed{-\frac{69}{28}} \]
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