Answer:
The solutions for y are:
For x = 0, any value of y will satisfy the equation.
For any other value of x, the solution for y is given by: y = (2x - 1)/2
Explanation:
To solve the equation x + y/x - y = 1/2 for y, we can follow these steps:
Multiply the entire equation by 2x to eliminate the denominators: 2x(x + y/x - y) = 2x(1/2).
Simplify the equation: 2x^2 + 2y - 2xy - 2y = x.
Combine like terms: 2x^2 - 2xy = x.
Move all terms to one side of the equation: 2x^2 - 2xy - x = 0.
Factor out a common factor of x: x(2x - 2y - 1) = 0.
Now, we have two possible solutions:
x = 0: If x = 0, then the equation becomes 0 = 0, which is true for any value of y.
2x - 2y - 1 = 0: Solve this equation for y: -2y = -2x + 1, y = (2x - 1)/2.
Therefore, the solutions for y are:
For x = 0, any value of y will satisfy the equation.
For any other value of x, the solution for y is given by: y = (2x - 1)/2