Need Help figuring out the following:

Simplying Complex Algebraic Fractions:

$\displaystyle \displaystyle \frac {y - \frac {x^2+y^2}{y}} {\frac {1}{x} - \frac {1}{y}}$

The book equates this to this:

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

It says in the book that this step reduces the numerator and denominator to single fractions. That's fine but doesn't say how it's done. I can see the top fraction you can get by:

$\displaystyle \displaystyle \frac {(y)(y)+(x^2+y^2)}{y}$

But i'm still unsure of that and don't know about the bottom fraction. I would normally look to multiply like

$\displaystyle \displaystyle \frac {(xy)(1)}{x} - \frac {(xy)(1)}{y}$

then cancel out the x and y's leaving:

$\displaystyle y-x$

Any suggestions advice would be great.

Cheers

BIOS