`3.bar4+5.bar8-7.bar9=`__

Options

A. `4//3`
B. `8//5`
C. `7//9`
D. `5//4`

Answer

To solve the expression \(3.\overline{4} + 5.\overline{8} - 7.\overline{9}\), we will convert each repeating decimal into a fraction and then perform the arithmetic operations.

### Step-by-Step Solution:

1. **Convert \(3.\overline{4}\) to a fraction:**
Let \(A = 3.\overline{4}\).
- Multiply both sides by 10:
\[ 10A = 34.\overline{4} \]
- Now, subtract \(A\) from \(10A\):
\[ 10A - A = 34.\overline{4} - 3.\overline{4} \]
\[ 9A = 34 - 3 \]
\[ 9A = 31 \]
- Therefore,
\[ A = \frac{31}{9} \]

2. **Convert \(5.\overline{8}\) to a fraction:**
Let \(B = 5.\overline{8}\).
- Multiply both sides by 10:
\[ 10B = 58.\overline{8} \]
- Now, subtract \(B\) from \(10B\):
\[ 10B - B = 58.\overline{8} - 5.\overline{8} \]
\[ 9B = 58 - 5 \]
\[ 9B = 53 \]
- Therefore,
\[ B = \frac{53}{9} \]

3. **Convert \(7.\overline{9}\) to a fraction:**
Let \(C = 7.\overline{9}\).
- Multiply both sides by 10:
\[ 10C = 79.\overline{9} \]
- Now, subtract \(C\) from \(10C\):
\[ 10C - C = 79.\overline{9} - 7.\overline{9} \]
\[ 9C = 79 - 7 \]
\[ 9C = 72 \]
- Therefore,
\[ C = \frac{72}{9} = 8 \]

4. **Combine the fractions:**
Now we need to compute \(A + B - C\):
\[ A + B - C = \frac{31}{9} + \frac{53}{9} - 8 \]
- First, combine \(A\) and \(B\):
\[ A + B = \frac{31 + 53}{9} = \frac{84}{9} \]
- Now subtract \(C\) (which is 8 or \(\frac{72}{9}\)):
\[ A + B - C = \frac{84}{9} - \frac{72}{9} = \frac{84 - 72}{9} = \frac{12}{9} \]

5. **Simplify the result:**
- Simplifying \(\frac{12}{9}\):
\[ \frac{12}{9} = \frac{4}{3} \]

### Final Answer:
Thus, the final result is:
\[ \boxed{\frac{4}{3}} \]