AHSME 1970 Problem 3

If $x=1+2^p$ and $y=1+2^{-p}$, then $y$ in terms of $x$ is $\text{(A) } \frac{x+1}{x-1} \text{(B) } \frac{x+2}{x-1} \text{(C) } \frac{x}{x-1} \text{(D) } 2-x \text{(E) } \frac{x-1}{x}$