From 1/x +1/(xy) = y, you want to find y in terms of x only.

Okay.

You then have to isolate the y's, and do anything to have "y" only on one side of the equation. That will get x on the other side.

1/x +1/(xy) = y

Clear the fractions, multiply both sides by xy,

y +1 = x*y^2

Umm, we are getting a quadratic equation in "y",

0 = x*y^2 -y -1

Or,

x*y^2 -y -1 = 0

Use the Quadratic Formula,

y = {-(-1) +,-sqrt[(-1)^2 -4(x)(-1)]} / (2*x)

y = {1 +,-sqrt[1 +4x]} / 2x ------------------****

That means,

y = [1 +sqrt(1+4x)]/(2x)

or, y = [1 -sqrt(1+4x)]/(2x)