Final answer:
To determine which solution contains an error, each equation must be solved by eliminating denominators, simplification, and solving for x. If an error exists, it likely lies in the algebraic manipulation or simplification process.
Step-by-step explanation:
To identify which solution contains an error, we need to evaluate each one step by step.
For the first equation \(3x + 4 = \frac{2}{x+2}\), if you clear the fraction by multiplying both sides by \(x+2\), you should get \(3x(x+2) + 4(x+2) = 2\), which would lead to a quadratic equation that can be solved for x.
The second equation \(\frac{8}{x-6} = \frac{3x+4}{x+2}\) can also be solved by multiplying both sides by the common denominator (\(x+2\))(\(x-6\)). Once you carry out the multiplication and simplification, you will get a quadratic equation. Check for errors in simplification or algebraic manipulation.
The third equation, \(\frac{80x+8}{(x+1)(x-6)} + \frac{1}{x+1} = \frac{2x-12}{(x+1)(x-6)}\), also involves working with common denominators and simplifying to solve for x. If there is a mistake, it may occur in the process of combining terms or simplifying the equation.
We would need do this analysis for each given equation to determine the one with an error.