Need help with finding tangent lines...

I have encountered this type of problem a few times in my class and need help:

Find the equation(s) of the tangent line(s) to the curve f(x)= x/(1-x) that is perpendicular to the line x + 2y = 4

Since the line "x + 2y = 4" has a slope of -.5, I'm guessing I have to find where on the curve f(x) the tangent line has a slope of 2. Would I just set up an equation where 2 is equal to the equation of the slope of the tangent line for f(x) and solve for x?

I got an answer this way but I'm not sure if that's the right way to do it...

Thanks