1976 AHSME Problems/Problem 1

Revision as of 21:48, 11 July 2020 by Mathjams (talk | contribs) (Solution)

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 $x=-2\Rightarrow \textbf{(A)}$.

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