Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.6 Junior Find the answer

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

Your answer

Multiple choice: answer with the letter of the option you want.

Solution

When $x=\frac{1}{2}$ , $\frac{x+1}{x-1}=-3$ , substituting $-3$ for $x$ in the original equation we get:
$\frac{-3+1}{-3-1}=\frac{-2}{-4}=\frac{1}{2}\implies \boxed{\mathbf{(E)}\text{ None of these}}$ .

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