Is it possible to simplify $\frac{2^{2x-1} - 2^{x-1}}{2^{2x-1}}$?

Question

Is it possible to simplify this expression?

$\frac{2^{2x-1} - 2^{x-1}}{2^{2x-1}}$

Answer 1

$$\begin{align}\frac{2^{2x-1} - 2^{x-1}}{2^{2x-1}} &=\frac{2^{2x-1}}{2^{2x-1}}-\frac{2^{x-1}}{2^{2x-1}} \\ &=1-2^{(x-1)-(2x-1)} \\ &=1-2^{-x} \end{align}$$

Answer 2

Yeah you can do this: $$\frac{ 2^{x-1} \Bigl[ 2^{x}-1\Bigr]}{2^{2x-1}} = \frac{2^{x}-1}{2^{x}}$$