To simplify the expression [tex]\(-\frac{3}{6} - \frac{5}{7}\)[/tex], follow these steps:
1. Find a Common Denominator: The denominators in this expression are 6 and 7. To add or subtract fractions, they must have a common denominator. The least common multiple (LCM) of 6 and 7 is 42.
2. Convert Each Fraction to the Common Denominator:
- For [tex]\(-\frac{3}{6}\)[/tex]:
- Multiply the numerator and the denominator by 7 to get the equivalent fraction with a denominator of 42.
[tex]\[
-\frac{3}{6} = -\frac{3 \times 7}{6 \times 7} = -\frac{21}{42}
\][/tex]
- For [tex]\(-\frac{5}{7}\)[/tex]:
- Multiply the numerator and the denominator by 6 to get the equivalent fraction with a denominator of 42.
[tex]\[
-\frac{5}{7} = -\frac{5 \times 6}{7 \times 6} = -\frac{30}{42}
\][/tex]
3. Subtract the Two Fractions:
- With the fractions now having the same denominator, you can subtract the numerators and keep the common denominator.
[tex]\[
-\frac{21}{42} - \frac{30}{42} = -\frac{21 + 30}{42} = -\frac{51}{42}
\][/tex]
4. Simplify the Fraction:
- To simplify [tex]\(-\frac{51}{42}\)[/tex], check if the numerator and the denominator have any common factors other than 1. In this case, they do not share a common factor other than 1. Therefore, [tex]\(-\frac{51}{42}\)[/tex] is already in its simplest form.
Hence, the simplified form of the expression [tex]\(-\frac{3}{6} - \frac{5}{7}\)[/tex] is [tex]\(-\frac{51}{42}\)[/tex].
