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Addition of Fractions

Evaluate 2+...

Question

Evaluate $2 + \frac{1}{1 - \frac{1}{1 - \frac{1}{3}}}$

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Solution

$= 2 + \frac{1}{1 - \frac{1}{1 - \frac{1}{3}}}$

$= 2 + \frac{1}{1 - \frac{1}{\frac{3 - 1}{3}}}$

$= 2 + \frac{1}{1 - \frac{1}{\frac{2}{3}}}$

$= 2 + \frac{1}{1 - \frac{3}{2}}$

$= 2 + \frac{1}{\frac{2 - 3}{2}}$

$= 2 + \frac{1}{\frac{- 1}{2}}$

$= 2 + \frac{2}{- 1}$

$= 2 + (- 2) = 0$

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