To solve the expression \(-\frac{1}{28} - \left(-\frac{1}{42}\right)\), follow these steps:
1. First, simplify the expression inside the parentheses:
[tex]\[
-\left(-\frac{1}{42}\right) = \frac{1}{42}
\][/tex]
2. Rewrite the original expression with this simplification:
[tex]\[
-\frac{1}{28} + \frac{1}{42}
\][/tex]
3. Next, find a common denominator for the fractions. The denominators are 28 and 42. The least common multiple (LCM) of 28 and 42 is 84.
4. Convert each fraction to have the common denominator of 84:
[tex]\[
-\frac{1}{28} = -\frac{1 \times 3}{28 \times 3} = -\frac{3}{84}
\][/tex]
[tex]\[
\frac{1}{42} = \frac{1 \times 2}{42 \times 2} = \frac{2}{84}
\][/tex]
5. Now, with a common denominator, add the two fractions:
[tex]\[
-\frac{3}{84} + \frac{2}{84} = \frac{-3 + 2}{84} = \frac{-1}{84}
\][/tex]
6. Thus, the result of the expression is:
[tex]\[
-\frac{1}{84}
\][/tex]
To summarize the steps clearly:
- Simplify \(-\left(-\frac{1}{42}\right)\) to \(\frac{1}{42}\).
- Find a common denominator for the fractions, converting them to \(-\frac{3}{84}\) and \(\frac{2}{84}\).
- Add these fractions to get \(\frac{-1}{84}\).
The final result is [tex]\(\boxed{-\frac{1}{84}}\)[/tex].
