Solve the equation 3/x + 2/x+1 = 1. What is the value of x?
- 2 + √7
- 3 + √7
- 4 + √7
- None of these
Explanation
Given equation:
3/x + 2/(x+1) = 1
Multiply both sides by x(x+1):
3(x+1) + 2x = x(x+1)
Expanding both sides:
3x + 3 + 2x = x² + x
Combine like terms:
5x + 3 = x² + x
Rearrange the equation:
x² - 4x - 3 = 0
Solve the quadratic equation:
x = (4 ± √(16 + 12)) / 2
x = (4 ± √28) / 2
x = (4 ± 2√7) / 2
x = 2 ± √7
The answer is 2 + √7 or 2 - √7.
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