Difference between revisions of "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 $x=-2\Rightarrow \textbf{(A)}$.~MathJams