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