# Thread: Can't figure out how these fractions were solved

1. ## Can't figure out how these fractions were solved

I am looking at a solution and can't figure out what was done to the fractions, there are two equations:

Would appreciate if you could help me understand this.

2. ## Re: Can't figure out how these fractions were solved

All the terms with V1 have been collected, all the terms with V2 have been collected, and everything else has been moved to the other side...

3. ## Re: Can't figure out how these fractions were solved

Originally Posted by Prove It
All the terms with V1 have been collected, all the terms with V2 have been collected, and everything else has been moved to the other side...
Alright that does sound easy, didn't know there was such thing we can do and it makes it a lot easier to deal with. Thanks a lot.
Now I have to solve them with simultaneous equations and I got the feeling that it's really going to look nasty and impossible to solve, is there a better way to do it ?

4. ## Re: Can't figure out how these fractions were solved

Well, after you add the fractions, each equation will be of the form $AV_1+ BV_2= C$. The numbers may be "bad" but you shouldn't be stopped by arithmetic!

5. ## Re: Can't figure out how these fractions were solved

Suggestions to "make the process" less unwieldy:
Change V1 to u and V2 to v.
Let a=2200, b=5600, c=3300, d=6800 (the 4 denominators).

Equations become:
(u-22)/a + (u+12)/b + (u-v)/c = 0 [1]
(v-6)/d + (v-u)/c = 0 [2]

Solve [2] for v, substitute in [1]

TIP: if a fraction = 0, then numerator = 0