1. Simplify the nested fraction:
$$\frac{2}{1 - \frac{1+x}{3}} = \frac{2}{\frac{3 - (1+x)}{3}} = \frac{6}{3 - 1 - x} = \frac{6}{2-x}$$
2. Substitute back into the equation: $$1 + \frac{3}{1 + \frac{6}{2-x}} = 3$$
3. Solve for x: $$1 + \frac{3}{\frac{2-x+6}{2-x}} = 3 \implies 1 + \frac{3(2-x)}{8-x} = 3 \implies \frac{3(2-x)}{8-x} = 2 \implies 6 - 3x = 16 - 2x \implies -10 = x$$
The correct option is not listed. Assuming there might be a typo in the problem or options, let's re-evaluate if the question implies a different structure or if there's a mistake in transcription. Given the options, let's check if any of them lead to a simpler solution or if there's a common pattern in such problems. However, based on direct algebraic manipulation, x = -10. Since -10 is not an option, and assuming the question is solvable with the given options, there might be an error in the problem statement or the provided options. If we assume the equation was intended to be simpler or the options are correct, we cannot proceed without further clarification or correction.