tricky factoring problem

[pinkcalculator]

Here's another problem that I'm so close to finishing it hurts. I'm supposed to find the inverse of the given function.
I'm just not sure when and where to factor.

f(x) = (2x-1)/(3x+4)
y= (2x-1)/(3x+4)
x=(2y-1)/(3y+4)
(3y+4)*x= 2y-1

3xy + 4x =2y -1

And then, I'm lost. Did I distribute too early? Should I have divided differently?
Any help would be greatly appreciated.

 

[wjm11]

I'm supposed to find the inverse of the given function.
I'm just not sure when and where to factor.

f(x) = (2x-1)/(3x+4)
y= (2x-1)/(3x+4)
x=(2y-1)/(3y+4)
(3y+4)*x= 2y-1

3xy + 4x =2y –1

Next, group y terms on the left side and everything else on the right:

3xy-2y = -4x-1

Factor out y:

y(3x – 2) = - (4x + 1)

Divide:

y = (4x + 1)/(2 – 3x)
f’(x) = (4x + 1)/(2 – 3x)