Subtract the sum of `(-4)/(7) and (5)/(14)` from the sum of `(9)/(14) and (23)/(14)`.

Answer

To solve the problem, we need to perform the following steps:

1. **Calculate the sum S1**: This is the sum of \(-\frac{4}{7}\) and \(\frac{5}{14}\).
2. **Calculate the sum S2**: This is the sum of \(\frac{9}{14}\) and \(\frac{23}{14}\).
3. **Subtract S1 from S2**: This will give us the final result.

Now, let's go through each step in detail:

### Step 1: Calculate S1
We need to find the sum of \(-\frac{4}{7}\) and \(\frac{5}{14}\).

To add these fractions, we need a common denominator. The least common multiple of 7 and 14 is 14.

Convert \(-\frac{4}{7}\) to a fraction with a denominator of 14:
\[ -\frac{4}{7} = -\frac{4 \times 2}{7 \times 2} = -\frac{8}{14} \]

Now we can add:
\[ S1 = -\frac{8}{14} + \frac{5}{14} = \frac{-8 + 5}{14} = \frac{-3}{14} \]

### Step 2: Calculate S2
Next, we find the sum of \(\frac{9}{14}\) and \(\frac{23}{14}\).

Since both fractions have the same denominator, we can add them directly:
\[ S2 = \frac{9}{14} + \frac{23}{14} = \frac{9 + 23}{14} = \frac{32}{14} \]

### Step 3: Subtract S1 from S2
Now, we need to subtract S1 from S2:
\[ S2 - S1 = \frac{32}{14} - \left(-\frac{3}{14}\right) = \frac{32}{14} + \frac{3}{14} = \frac{32 + 3}{14} = \frac{35}{14} \]

### Simplifying the Result
Now, we can simplify \(\frac{35}{14}\):
\[ \frac{35}{14} = \frac{35 \div 7}{14 \div 7} = \frac{5}{2} \]

### Final Result
Thus, the final result is:
\[ \frac{5}{2} \text{ or } 2.5 \]