To solve the problem, we need to simplify the expression:
\(\frac{(3+7)\times2-4}{(3+7)\times(2-4)}+\frac{3+7\times2-5}{3+7\times(2-5)}\)
Step-by-step Simplification:
- First Fraction:
- Numerator: \((3+7)\times2-4 = 10\times2-4 = 20-4 = 16\)
- Denominator: \((3+7)\times(2-4) = 10\times(-2) = -20\)
- The first fraction is: \(\frac{16}{-20} = -\frac{4}{5}\).
- Second Fraction:
- Numerator: \(3+7\times2-5 = 3+14-5 = 12\)
- Denominator: \(3+7\times(2-5) = 3+7\times(-3) = 3-21 = -18\)
- The second fraction is: \(\frac{12}{-18} = -\frac{2}{3}\).
- Combine the fractions:\[-\frac{4}{5} + \left(-\frac{2}{3}\right)\]
- Find a common denominator: The LCM of 5 and 3 is 15.
- Rewrite the fractions:\[-\frac{4}{5} = -\frac{4\times3}{5\times3} = -\frac{12}{15},\quad -\frac{2}{3} = -\frac{2\times5}{3\times5} = -\frac{10}{15}\]
- Combine: \[-\frac{12}{15} - \frac{10}{15} = -\frac{22}{15}\]
Therefore, the correct answer is \(-\frac{22}{15}\).