(1 / x) + (1 / (x - 4)) = (x - 3) / (x - 4)
((x - 4) / (x(x - 4))) + (x / (x(x - 4))) = x(x - 3) / (x(x - 4))
(x - 4) + x = x(x - 3)
2x - 4 = x^2 - 3x
x^2 - 3x - 2x + 4 = 0
x^2 - 5x + 4 = 0
(x - 4)(x - 1) = 0
x - 4 = 0 or x - 1 = 0
x = 4 or x = 1
However, x - 4 is in the denominator of the fraction (x - 3) / (x - 4), so we need to reject it, or we will be dividing by zero.
Hence, the only answer is x = 1.