AHSME 1967 Problem 2

An equivalent of the expression $\left(\frac{x^2+1}{x}\right)\left(\frac{y^2+1}{y}\right)+\left(\frac{x^2-1}{y}\right)\left(\frac{y^2-1}{x}\right)$, $xy \not= 0$, is: $\text{(A)}\ 1 \text{(B)}\ 2xy \text{(C)}\ 2x^2y^2+2 \text{(D)}\ 2xy+\frac{2}{xy} \text{(E)}\ \frac{2x}{y}+\frac{2y}{x}$