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Add [tex]-\frac{12}{7}+\left(\frac{3}{14}\right)[/tex]. Write your answer as a reduced improper fraction.

[tex]-\frac{12}{7}+\left(\frac{3}{14}\right)[/tex]

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Answer :

Let's work through adding the given fractions step by step. We'll add the fractions [tex]\(-\frac{12}{7}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex].

1. Find a common denominator:
The lowest common denominator (LCD) of 7 and 14 is 14.

2. Convert fractions to have the common denominator:
[tex]\(-\frac{12}{7}\)[/tex] can be converted to have a denominator of 14. We do this by multiplying both the numerator and denominator by 2:
[tex]\[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \][/tex]

3. Rewrite the fractions with the common denominator:
Now we have:
[tex]\[ -\frac{24}{14} \quad \text{and} \quad \frac{3}{14} \][/tex]

4. Add the fractions:
Since the denominators are the same, we can simply add the numerators:
[tex]\[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \][/tex]

5. Simplify the result:
The fraction [tex]\(\frac{-21}{14}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 7:
[tex]\[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \][/tex]

So, the sum of [tex]\(-\frac{12}{7}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex] is [tex]\(\frac{-3}{2}\)[/tex], a reduced improper fraction.

[tex]\[ \boxed{-\frac{3}{2}} \][/tex]