If $x, y$, and $y-\frac{1}{x}$ are not $0$, then
$\frac{x-\frac{1}{y}}{y-\frac{1}{x}}$ equals
$\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }\frac{x}{y} \qquad \mathrm{(C) \ } \frac{y}{x}\qquad \mathrm{(D) \ }\frac{x}{y}-\frac{y}{x} \qquad \mathrm{(E) \ } xy-\frac{1}{xy}$
Multiply the expression by $\frac{xy}{xy}$ to get rid of the fractional [numerator](https://artofproblemsolving.com/wiki/index.php/Numerator) and [denominator](https://artofproblemsolving.com/wiki/index.php/Denominator): $\frac{x^2y-x}{xy^2-y}$. This can be [factored](https://artofproblemsolving.com/wiki/index.php/Factoring) as $\frac{x(xy-1)}{y(xy-1)}$. The $xy-1$ terms cancel out, leaving $\frac{x}{y}, \boxed{\text{B}}$.