Question

\(\frac{(3+7)\times2-4}{(3+7)\times(2-4) }+\frac{3+7\times2-5}{3+7\times(2-5)}\)

• A. \(2\)
• B. \(-\frac{2}{5}\)
• C. \(-\frac{22}{15}\)
• D. \(-\frac{7}{5}\)

Answer 1

The Correct Option is C

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 \(-\frac{22}{15}\).