giving the following:

$\displaystyle ln|y| - ln|y-1| = ln|x| + K$

where K is the combined constant of integration from both sides

now when I take the exponential, I think I have to raise e to the entire

right side and that I can't do it term by term which simplifies to a division

using log properties and then canceling out the e and ln

$\displaystyle |\frac{y}{y-1}| = |x|e^{K}$

now I was thinking I could drop all the absolute values if I throw a +\-

in front of the remaining exponential, so we'll say $\displaystyle C=\pm e^{K}$

$\displaystyle \frac{y}{y-1} = Cx$