To solve this equation, we need to cross multiply:

(x + 1)(3x + 1) = (2x - 1)(x - 1)

Expanding both sides:

3x^2 + x + 3x + 1 = 2x^2 - 2x - x + 1

Combining like terms:

3x^2 + 4x + 1 = 2x^2 - 3x + 1

Subtracting (2x^2 - 3x + 1) from both sides:

3x^2 + 4x + 1 - 2x^2 + 3x - 1 = 0

x^2 + 7x = 0

This simplifies to:

x(x + 7) = 0

Therefore, the solutions for x are:

x = 0 or x = -7