1976 AHSME Problems/Problem 1

Problem 1

If one minus the reciprocal of $(1-x)$ equals the reciprocal of $(1-x)$ , then $x$ equals

$\textbf{(A) }-2\qquad \textbf{(B) }-1\qquad \textbf{(C) }1/2\qquad \textbf{(D) }2\qquad \textbf{(E) }3$

Solution

The reciprocal of $(1-x)$ is $\frac{1}{1-x}$ , so our equation is $1-\frac{1}{1-x}=\frac{1}{1-x},$ which is equivalent to $\frac{1}{1-x}=\frac{1}{2}$ . So, $1-x=2$ and $x=-2\Rightarrow \boxed{A}$ .

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1976 AHSME Problems/Problem 1

Problem 1

Solution