# Very simple fraction simplification

I feel stupid asking this, but I just can't see it. I need to simply this and I already know the answer, but I don't know why this is the answer.

simplify

3p-3q
5p-5q

My first reaction was to remove a factor of p-q but that would leave

p-q(3-3)
p-q(5-5)

Which would be 0/0. I know the answer is 3/5 but I just can't see why.

## Answers and Replies

CAF123
Gold Member
You can factor out p-q top and bottom, but your end result is not quite right. If you try to use the distributive law here, that is a(b+c) = ab + ac, this might help you see your error.

Mark44
Mentor
I feel stupid asking this, but I just can't see it. I need to simply this and I already know the answer, but I don't know why this is the answer.

simplify

3p-3q
5p-5q

My first reaction was to remove a factor of p-q but that would leave

p-q(3-3)
p-q(5-5)
The above is incorrect, and simplifies to 1, assuming p ≠ 0. This is based on what you wrote, which might not be what you intended.

The simplest way to go would be to notice that 3 is a factor of the terms in the numerator, and that 5 is a factor of the terms in the denominator. The original expression can be written like so:
$$\frac {3(p - q)}{5(p - q)}$$
Of course, this can be simplified further.
Which would be 0/0. I know the answer is 3/5 but I just can't see why.

That makes perfect sense now. Thanks for explaining it.