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your 1st step has an error:\[\frac{a}{2}+\frac{1}{4}=\frac{2a}{4}+\frac{1}{4}\ne\frac{3a}{4}\]

do you understand why?

Not sure .. now I'm confused LOL

look at the numerators of that fraction:
2a + 1 = ?

it would just be 2a + 1 / 4

because 2a and 1 are separate

yes - that is right

So then it would be 2a + 1/4 divided by 2a - 3 / 6

your 2nd step was correct:\[\frac{a}{3}-\frac{1}{2}=\frac{2a-3}{6}\]

your 3rd step has an error

then 2a + 1 / 4 * 6 / 2a - 3

yea I saw my error from the first part and realized I made the same mistake and then corrected it

ok - so you know what to do now and understand the process?

Now I am unsure of the rest ...

:) np - just let me know what part is troubling you...

yes

(2a + 1)*3 / 2*(2a - 3) = 6a + 3 / 4a - 6 ?

that is correct. although I would leave it in the form:\[\frac{3(2a+1)}{2(2a-3)}\]

haha yea i just noticed it was already reduced and doing what I did, UN-reduced it LOL

gr8! the good thing is that you recognised your mistakes - which is vital if you want to improve! :D

I second guess myself all the time and change things when they don't need changed or over-think it!

You're as "young" as you feel! take care and have a blessed day =) =)

thx - you too my friend! :)