Trouble with Rational Expression Division

Hello, everybody. I attempted to solve a rational expression which requires division and apparently got the wrong answer. Here's the expression:

$\displaystyle

\frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}

$

The steps I followed are as such:

1. (Turn it into multiplication):

$\displaystyle

\frac {x^2 - y^2}{xy} * \frac {y}{x - y}

$

$\displaystyle

\frac {y(x^2 - y^2)}{xy(x - y)}

$

2. Multiply:

$\displaystyle

\frac {yx^2 - y^3}{yx^2 - xy^2}

$

3. Simplify:

$\displaystyle

\frac {y}{x}

$

However, I checked the answer and apparently it's:

$\displaystyle

\frac {x + y}{x}

$

I'm not sure what exactly I did wrong in solving that rational expression, but any assistance in figuring it out would be greatly appreciated. :] Thank you guys for your time.

Colton