AHSME 1969 Problem 29

If $x=t^{1/(t-1)}$ and $y=t^{t/(t-1)},t>0,t \ne 1$, a relation between $x$ and $y$ is: $\text{(A) } y^x=x^{1/y} \text{(B) } y^{1/x}=x^{y} \text{(C) } y^x=x^y \text{(D) } x^x=y^y \text{(E) none of these}$