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Ahhh... so because -c/a have "no value" or are just equal to 1, we can manipulate them how we want?

Ah I'm sorry bob, but I don't think you're getting what I'm trying to say. I think I have a better way to explain it, check this out.

What I can't figure out is how the common denominator of 4a is gotten. Let me give an example. Lets say we want to add together 1/4 and 5/8. We would look of course at the multiples of 4 and find one that's equal to other denominator. So we find that 8 is the least common denominator for both fractions. We multiply 1/4 by 2/2 to get 2/8, and now we can solve.

My problem is how do we get the common denominator of 4a from -c/a? Like I said earlier, a variable without a coefficient has an implied coefficient of 1. So now we can look at -c/a as -1c/1a. How can we get the common denominator of 4 from 1, when 1 only has itself as a multiple? If both of the bases were the same we could just say it was equal to 1, divide that in half to get 5/10, get 1/2, and THEN we could have gotten the common denominator of 4. I don't see how this works.

Ah, so let me try something here.

So any variable without a coefficient has an implied value of 1 right? So based on that we can look at -c/a as -1c/1a. Now, from 1a we just get 4a/4a? That can't be right though. How can you get 4a/4a from 1a? 1 only has itself as a multiple. Do you understand what I mean?

I'm sorry but when I get stuck on something like this in math I just get fixated on it. I could just take the answer as it is but I NEED to know why it happens.

Alright let me start from the beginning.

So we have

What I do here first is I move the "loose" number over to right.

Now we have

Now I take the coefficient on

and divide it through the entire equation.Now my method tells me that I take half of the middle term, square it and then add it to both sides.

We end up with this.

This is where I got stuck. I don't know how to get the common denominator of 4a for -c/a. I hope I wrote everything out correctly as I was doing this through memory, and keeping track of exponents and what not can be a little tough when typing it out lol.

**geramul**- Replies: 16

I have only one question for this.

Let me write this out a little bit into the process already.

Alright so we have

What I want to know is how the common denominator for -c/a is gotten. I thought I had figured it out, but I'm pretty sure I was on the far side of mars in relation to how close I actually was to figuring it out. I THOUGHT, that since a variable with no coefficient has an implied value of 1, that I could turn -c/a into -c/2a that way, therefore gaining the ability to get the common denominator of 4a. This is wrong though I'm pretty sure.

I'm out of ideas at the moment. I need to step away from this and think some more . I would appreciate if someone could explain the process of how -c/a gets the common denominator of 4a.

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