1958 AHSME Problem 46

For values of x less than 1 but greater than -4, the expression \frac{x^2 - 2x + 2}{2x - 2} has:

\begin{array}{l} \textbf{(A)}\ \text{no maximum or minimum value}\qquad \\ \textbf{(B)}\ \text{a minimum value of }{+1}\qquad \\ \textbf{(C)}\ \text{a maximum value of }{+1}\qquad \\ \textbf{(D)}\ \text{a minimum value of }{-1}\qquad \\ \textbf{(E)}\ \text{a maximum value of }{-1} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.