1958 AHSME Problems/Problem 4

Problem

In the expression $\frac{x + 1}{x - 1}$ each $x$ is replaced by $\frac{x + 1}{x - 1}$ . The resulting expression, evaluated for $x = \frac{1}{2}$ , equals:

$\textbf{(A)}\ 3\qquad \textbf{(B)}\ -3\qquad \textbf{(C)}\ 1\qquad \textbf{(D)}\ -1\qquad \textbf{(E)}\ \text{none of these}$

Solution

When $x=\dfrac{1}{2}$ , $\dfrac{x+1}{x-1}=-3$ , substituting $-3$ for $x$ in the original equation we get:

$\dfrac{-3+1}{-3-1}=\dfrac{-2}{-4}=\dfrac{1}{2}\implies \boxed{\mathbf{(E)}\text{ None of these}}$ .

1958 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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1958 AHSME Problems/Problem 4

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