The value of 12-12-(1)/(2-12) is

1975 AMC 12 Problem 1

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The value of

\frac{1}{2-\dfrac{1}{2-\dfrac{1}{2-\frac12}}}

\frac34

\frac45

\frac56

\frac67

\frac65

Evaluate the nested denominator from the inside outward

The three successive inner values are

\frac32,\frac43,

and

\frac54

Working outward,

\begin{aligned} 2-\frac12&=\frac32,\\ 2-\frac1{\frac{3}{2}}&=\frac43,\\ 2-\frac1{\frac{4}{3}}&=\frac54. \end{aligned}

The given value is therefore

\frac{1}{\frac{5}{4}}=\frac{4}{5}.

Therefore, the correct answer is B.