1956 AHSME Problems/Problem 12

If $x^{ - 1} - 1$ is divided by $x - 1$ the quotient is:

$\textbf{(A)}\ 1\qquad \textbf{(B)}\ \frac{1}{x-1}\qquad \textbf{(C)}\ \frac{-1}{x-1}\qquad \textbf{(D)}\ \frac{1}{x}\qquad \textbf{(E)}\ -\frac{1}{x}$

Solution

We write $x^{-1} - 1 = \frac{1}{x} - 1 = \frac{1-x}{1} = -\frac{1}{x}(x - 1)$. This means that our answer is $\boxed{\textbf{(E)}}$, and we are done.

See also

1956 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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