Hello.

I'm currently going through I.M Gelfand and A. Shen's "Algebra".

The section I'm on is about converting rational expressions to quotients of two polynomials.

The book shows how to do the transformations.

e.g.

$\displaystyle \frac{P}{Q} + \frac{R}{S} = \frac{PS}{QS} + \frac{QR}{QS} = \frac{PS + QR}{QS}$ where P,Q,R and S are polynomials. That I understand.

All make sense to me but the last which is for division:

$\displaystyle \frac{P}{Q} / \frac{R}{S} = \frac{PS}{QR}$

Can anyone explain why that is so? Or do I just need to work on dealing with fractions?