Simplify $\dfrac{2^{-1} - 4^{-1}}{2^{-1} + 4^{-1}}$.

Simplify $\dfrac{2^{-1} - 4^{-1}}{2^{-1} + 4^{-1}}$.
  1. $\dfrac{1}{3}$
  2. $3$
  3. $\dfrac{2}{3}$
  4. $\dfrac{4}{3}$

Solution

Numerator: $\dfrac{1}{2} - \dfrac{1}{4} = \dfrac{1}{4}$. Denominator: $\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4}$. Ratio: $\dfrac{1/4}{3/4} = \dfrac{1}{3}$.

Asked in: IMO

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