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.