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jmc

algebra junior

Problem

Compute

\frac{2 + 4 - 8 + 16 + 32 - 64}{4 + 8 - 16 + 32 + 64 - 128}

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Solution

Factoring the numerator and denominator, we have:

\frac{2 + 4 - 8 + 16 + 32 - 64}{4 + 8 - 16 + 32 + 64 - 128} = \frac{2 ( 1 + 2 - 4 + 8 + 16 - 32 )}{4 ( 1 + 2 - 4 + 8 + 16 - 32 )} = \frac{2}{4} = \frac{1}{2}

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Final answer

\frac{1}{2}