Question

Solve the equation (2x) / (3x+y) =y using the quotient rule. What is the correct solution for x in terms of y after solving the equation?

Answer 1

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:

1. Multiply both sides by the denominator (3x+y) to get rid of the fraction: 2x = y(3x + y).
2. Distribute y on the right side: 2x = 3xy + y².
3. Get all terms involving x on one side: 2x - 3xy = y².
4. Factor out x on the left side: x(2 - 3y) = y².
5. 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).