Final answer:
The solution for the equation (2x) / (3x+y) = y is found by algebraic manipulation, resulting in x = y² / (2 - 3y), where 2 - 3y is not equal to zero.
Step-by-step explanation:
To solve the equation (2x) / (3x+y) = y for x in terms of y, we can use algebraic manipulation. Here is a step-by-step guide to solving this equation:
- Multiply both sides by the denominator (3x+y) to get rid of the fraction: 2x = y(3x + y).
- Distribute y on the right side: 2x = 3xy + y².
- Get all terms involving x on one side: 2x - 3xy = y².
- Factor out x on the left side: x(2 - 3y) = y².
- Divide both sides by (2 - 3y) to solve for x: x = y² / (2 - 3y), assuming 2 - 3y is not equal to zero since we cannot divide by zero.
The correct solution for x in terms of y is x = y² / (2 - 3y).