# Math Help - Help me understand why p over q over...

1. ## Help me understand why p over q over...

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.

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

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

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

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

2. When dividing fractions, flip and multiply.

So, $\frac {P}{Q} /\frac {R}{S}$ becomes $\frac {P}{Q} \cdot \frac {S}{R}$

3. That's right! Not sure how I managed to forget that. Slightly embarrassing really. Thanks so much for the speedy reply as well.