solve this for y: x=(y+3)/(y-2)?

Answer 1

x = (y+3)/(y-2)
Multiply both sides by (y-2)
x(y-2) = y + 3
Distribute the x on the left side
xy - 2x = y +3
Subtract y from both sides and add 2x to both sides
xy - y = 2x + 3
Factor out the y on the left side
y(x-1) = 2x+3
Divide both sides by (x-1)
y = (2x+3)/(x-1)

Answer 2

You can use any of the two answers given above. The second solution is just another way of expressing the answer. If you multiply the second answer with (-1)/(-1) you will get the same answer as in the first solution.
I prefer the first solution because it is simpler.
x (y - 2) = (y + 3)
xy - 2x = y + 3
xy - y = 2x + 3
y (x - 1) = 2x + 3
y = (2x + 3)/(x-1)

Answer 3

x=(y+3)/(y-2)

xy - 2x = y + 3

y - xy = -2x - 3

y (1 - x) = -(2x + 3)

y = - (2x + 3) / (1 - x)