The problem asks to solve the following expression for y in terms of x if x is not equal to zero and y is not equal to zero:
1/X + 1/XY =y
THanks
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)