Simplifying Rational Expressions, I don't understand how they got this answer?

Question

anonymous · Answer

$$2p-24\div 4p-48$$ This is the original problem.

anonymous · Answer

First I canceled out the 24 and divided 48 by 24 to get 2. then i cancelled out 2p and divided 4p and got 2.

anonymous · Answer

$$1-1/2-2$$ This is the answer I got.

anonymous · Answer

The book has 1/2 written as the answer.I don't understand that.

anonymous · Answer

@Mertsj

mertsj · Answer

$$\frac{2p-24}{4p-48}$$

mertsj · Answer

First you must know that only factors may be cancelled.  That's why you are having trouble.  You cancelled addends.

mertsj · Answer

So before you can cancel, you have to factor the numerator and denominator.

mertsj · Answer

$$\frac{2x-24}{4x-48}=\frac{2(x-12)}{4(x-12)}$$

mertsj · Answer

Now...those are factors and can be cancelled.  Can you finish it?

anonymous · Answer

Ok, I get that :) Thank you for showing me :)

mertsj · Answer

yw