Final answer:
To solve the equation 2/x - 1 = 3/(3x - 3) + 1/6, we must first find and use a common denominator to combine terms and eliminate fractions, leading to a simplified equation that can be solved for x.
Step-by-step explanation:
The equation provided by the student is 2/x - 1 = 3/(3x - 3) + 1/6. To solve for x, we need to find a common denominator and combine the terms on the right side of the equation. The common denominator for 3x - 3 and 6 is 6(3x - 3). Multiplying both sides of the equation by this common denominator will remove the fractions and simplify the equation.
After simplifying, we get a linear equation in one variable that we can solve for x. The steps involve distributing the common denominator, combining like terms, and then isolating x to one side of the equation.