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

Algebra ->  Divisibility and Prime Numbers -> 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      Log On


   



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

+%286%2F%283x-2%29%29+%2B+%283%2F2x%29+

if we had +2%2F3+%2B+1%2F4+ 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:

+%282%2F3%29%284%2F4%29+%2B+%281%2F4%29%283%2F3%29+
+%288%2F12%29+%2B+%283%2F12%29+
+%2811%2F12%29+

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

We can multiply the numerators together and the denominators too:
+%286%282x%29%29%2F%28%282x%29%283x-2%29%29+%2B+%283%283x-2%29%29%2F%282x%283x-2%29%29+
And now add them together since they have the same denominator:
+%286%282x%29+%2B+3%283x-2%29%29%2F%28%282x%29%283x-2%29%29+

So that is the fractions done. The rest is just manipulation of the algebra to try to simplify it:
+%2812x+%2B+3%283x-2%29%29%2F%28%282x%29%283x-2%29%29+
+%2812x+%2B+9x-6%29%2F%28%282x%29%283x-2%29%29+
+%2821x-6%29%2F%28%282x%29%283x-2%29%29+

or perhaps multiply out the denominator:
+%2821x-6%29%2F%286x%5E2-4x%29+

but we tend not to do this - we like things factorised. The answer is best quoted as +%2821x-6%29%2F%28%282x%29%283x-2%29%29+

hope this helps
cheers
Jon.