Note that x cannot be 1/4, since 4x - 1 is in the denominator.
3 / (4x - 1) = (2 + x) / 3
9 / [3(4x - 1)] = [(2 + x)(4x - 1)] / [3(4x - 1)]
9 = (2 + x)(4x - 1)
9 = 8x + 4x^2 - 2 - x
4x^2 + 7x - 11 = 0
4x^2 + 11x - 4x - 11 = 0
(4x^2 + 11x) - (4x + 11) = 0
x(4x + 11) - (1)(4x + 11) = 0
(4x + 11)(x - 1) = 0
4x + 11 = 0 or x - 1 = 0
x = -11/4 or x = 1