Simplify: ${[1 - 2 (1 - 2)^{- 1}]}^{- 1}$

\frac{1}{3}

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- \frac{1}{3}

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- 1

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\frac{1}{2}

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Solution

The correct option is A $\frac{1}{3}$
${[1 - 2 {(1 - 2)}^{- 1}]}^{- 1} = {[1 - 2 {(- 1)}^{- 1}]}^{- 1}$

$= {[1 - 2 \times \frac{1}{- 1}]}^{- 1} = {[1 + 2]}^{- 1} = 3^{- 1} = \frac{1}{3}$

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