I'm currently working on algebraic manipulation, changing algebraic fractions into a chosen alternate form but I've hit a brick wall. 

I'm trying to get: 
$$\frac{2(3^x - 2^x)}{3^{x+1} - 2^{x+1}}$$ 

to the alternate form: 

$$\frac{2}{\frac{1}{(3/2)^x-1}+3}$$

Any help will be seriously appreciated!