Quick and simple maths question

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I know there's some math geniuses on this board and I don't want this to be seen as a 'do my homework' for my thread, more like an 'explain my homework!'. I'm currently studying a long distance Math course and as I haven't done any for several years I'm struggling to remember some of the algebra I learnt in school.
I'm currently simplyfying expresions and have been doing fine up until now, but I can't for the life figure out how to do it when there is division involved and my google skills are clearly weak.

This is not the exact question but could someone show me how you would go about simplyfing the following:

(4-6x)/2 + 2

Using www.wolframalpha.com I can see that it's alternate form is 4 - 3x but I can't get my head around the working and can't see it explained in my study books.

Thanks in advance
 
(4-6x)/2 is just a fraction. You can split it up into: 4/2 -(6x)/2

Imagine doing it with just numbers, for example:

(4-2)/2 is the same as saying 2/2 if you simplify the top of the fraction. But instead you could have "split" the fraction, ie:

4/2 - 2/2 = 2 - 1 = 1

You can apply the same "intuitive" fraction rules you use with numbers to algebraic letters. :)
 
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(a-b)/c = a/c - b/c and, equivalently, c(a-b) = ac - bc

When you divide something in brackets, it's the same as dividing each thing inside the brackets seperately.
 
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