What is the solution for x in the equation 1/(x - 4) + 1/3 = 3/(3x - 12)?

To solve the equation ( \frac{1}{x - 4} + \frac{1}{3} = \frac{3}{3x - 12} ), we first simplify the right-hand side. Noticing that ( 3x - 12 ) can be factored as ( 3(x - 4) ), we rewrite the equation:

[

\frac{1}{x - 4} + \frac{1}{3} = \frac{3}{3(x - 4)}

]

The right-hand side simplifies to:

[

\frac{3}{3(x - 4)} = \frac{1}{x - 4}

]

Substituting this back into the equation gives us:

[

\frac{1}{x - 4} + \frac{1}{3} = \frac{1}{x - 4}

]

Next, we can subtract ( \frac{1}{x - 4} ) from both sides:

[

\frac{1}{3} = 0

]

This is a contradiction because ( \frac{1}{3} ) cannot equal zero. This outcome indicates that there are