Here are the steps to solve this problem:

y=3x/x+1

When finding the inverse of a function, all the "y"s are replaced by "x" and vice versa. That's why it's called the inverse.

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

The inverse of that is:

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

x(y+1) = 3y

xy + x = 3y      (Which is what you were at)

x = 3y - xy       (Move the term xy)

x = y(3 - x)       (Factor out y)

y = x / (3 - x)    (Move the term 3-x to isolate y)

And that's the inverse! Hope that helps, let me know if it didn't! :)