A complex fraction is one which has fractional parts in the numerator or the denominator. For example, the following is a complex fraction:

\[ \frac{1}{1-\frac{1}{3}}. \]

To work with complex fractions, we just need to begin with the most deeply nested fraction and simplify from there. Thus,

\[ \frac{1}{1 - \frac{1}{3}} = \frac{1}{1 - \frac{1}{3} } \times \frac{3}{3} = \frac{3}{ 3 - 1 } = \frac{3}{2}. \]

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