Evaluate:
`((15)/(35)xx(26)/(24))-[((16)/(-21)xx(69)/(64))-((5)/(44)div(35)/(99))]`

Answer

To evaluate the expression

\[ \left(\frac{15}{35} \times \frac{26}{24}\right) - \left(\left(\frac{16}{-21} \times \frac{69}{64}\right) - \left(\frac{5}{44} \div \frac{35}{99}\right)\right) \]

we will follow these steps:

### Step 1: Simplify the first part of the expression

Calculate \(\frac{15}{35} \times \frac{26}{24}\).

1. Simplify \(\frac{15}{35}\):
\[ \frac{15}{35} = \frac{3}{7} \quad (\text{dividing both numerator and denominator by 5}) \]

2. Simplify \(\frac{26}{24}\):
\[ \frac{26}{24} = \frac{13}{12} \quad (\text{dividing both numerator and denominator by 2}) \]

3. Now multiply the simplified fractions:
\[ \frac{3}{7} \times \frac{13}{12} = \frac{3 \times 13}{7 \times 12} = \frac{39}{84} \]

### Step 2: Simplify the second part of the expression

Calculate \(\left(\frac{16}{-21} \times \frac{69}{64}\right) - \left(\frac{5}{44} \div \frac{35}{99}\right)\).

1. Calculate \(\frac{16}{-21} \times \frac{69}{64}\):
- Simplify \(\frac{69}{64}\) (no simplification needed here).
- Multiply:
\[ \frac{16 \times 69}{-21 \times 64} = \frac{1104}{-1344} \]
- Simplifying \(\frac{1104}{1344}\) gives:
\[ \frac{1104 \div 48}{1344 \div 48} = \frac{23}{28} \quad (\text{after simplifying}) \]
- So, we have:
\[ \frac{23}{-28} = -\frac{23}{28} \]

2. Calculate \(\frac{5}{44} \div \frac{35}{99}\):
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{5}{44} \times \frac{99}{35} = \frac{5 \times 99}{44 \times 35} \]
- Simplifying:
\[ \frac{5 \times 99}{44 \times 35} = \frac{495}{1540} \]
- Simplifying \(\frac{495}{1540}\) gives:
\[ \frac{495 \div 5}{1540 \div 5} = \frac{99}{308} \]

### Step 3: Combine the results

Now we combine the results from Step 1 and Step 2:
\[ \frac{39}{84} - \left(-\frac{23}{28} - \frac{99}{308}\right) \]

1. Convert \(-\frac{23}{28}\) to have a common denominator with \(\frac{99}{308}\):
- The LCM of 28 and 308 is 308.
- Convert:
\[ -\frac{23}{28} = -\frac{23 \times 11}{28 \times 11} = -\frac{253}{308} \]

2. Now combine:
\[ -\frac{253}{308} - \frac{99}{308} = -\frac{352}{308} \]

### Step 4: Final calculation

Now we have:
\[ \frac{39}{84} + \frac{352}{308} \]

1. Convert \(\frac{39}{84}\) to have a common denominator of 308:
- The LCM of 84 and 308 is 308.
- Convert:
\[ \frac{39 \times 4}{84 \times 4} = \frac{156}{308} \]

2. Now combine:
\[ \frac{156}{308} + \frac{352}{308} = \frac{508}{308} \]

3. Simplify \(\frac{508}{308}\):
- Dividing both by 4:
\[ \frac{127}{77} \]

### Final Answer

The final answer is:
\[ \frac{127}{77} \]