SOLUTION: Hi there, I have to express my answer in simplest form after adding this problem. The problem reads like this: 6/3x-2 + 3/2x. I'm not even really sure what to do, so any help

Question 88232: Hi there,
I have to express my answer in simplest form after adding this problem. The problem reads like this: 6/3x-2 + 3/2x.
I'm not even really sure what to do, so any help you can give me would be greatly appreciated!
Thank you so much!!

Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
this is just a fraction problem. We treat it just like numerical fractions:

if we had we would have to find the LCM of both 3 and 4 --> 3*4 which we can evaluate --> 12.
We do the same with (3x-2) and 2x. Their LCM is (3x-2)*2x which we cant evaluate so we leave it like that.

Next step is to multiply both fractions by 1 (so they remain unchanged) but write the 1 as a fraction:

Algebraically we cannot do all these steps. We can do the first one:

We can multiply the numerators together and the denominators too:

And now add them together since they have the same denominator:

So that is the fractions done. The rest is just manipulation of the algebra to try to simplify it:

or perhaps multiply out the denominator:

but we tend not to do this - we like things factorised. The answer is best quoted as

hope this helps
cheers
Jon.

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