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Is it possible to simplify this expression?

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

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Try… – lhf Mar 18 '11 at 14:38
Remember if you ever have a "is it possible" question, try wolfram alpha first! – Samuel Reid Jan 2 '12 at 5:19
up vote 8 down vote accepted

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

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

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or $1-2^{-x}$ . – lhf Mar 18 '11 at 14:41

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