Solve the equation: 1/x + 1/(x + 2) = 5/12.
Answer and explanation
Correct answer: D. x = 4 or x = -6/5
- Step 1: Combine left side: (x + 2 + x) / (x(x + 2)) = (2x + 2) / (x^2 + 2x). Step 2. Cross-multiply with 5/12: 12(2x + 2) = 5(x^2 + 2x) => 24x + 24 = 5x^2 + 10x. Step 3. Rearrange: 5x^2 - 14x - 24 = 0 => (5x + 6)(x - 4) = 0. Step 4. Solutions are x = 4 or x = -6/5. Answer: x = 4 or x = -6/5. Why not the others: The other factorings do not give 5x^2 - 14x - 24 = 0.
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