Solving for 2-2^-x in 1/2^x+(2^(x)-1)/2^(x-1)

[jackscholar]

Homework Statement

I need to get 1/2^x+(2^(x)-1)/2^(x-1) to equal 2-2^-x
I originally used index laws so 2^-x+2^(1-x)[2^x - 1]
From there i expanded so that 2^-x + 2 - 2^(1-x) was the result, I'm not sure where to go from here

 

[Sunil Simha]

try bringing the 2^-x on the RHS to the LHS and then proceed. No need to use index laws here till the very end.

 

[SammyS]

Homework Statement

I need to get 1/2^x+(2^(x)-1)/2^(x-1) to equal 2-2^-x
I originally used index laws so 2^-x+2^(1-x)[2^x - 1]
From there i expanded so that 2^-x + 2 - 2^(1-x) was the result, I'm not sure where to go from here

I assume you want to show that $\displaystyle \ \ 2^{-x}+\frac{2^{x}-1}{2^{x-1}}=2-2^{-x}\ .$

Your result looks correct so far.

Factor a 2 out of $\displaystyle \ \ 2^{1-x}\ .$