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    Why can't 6 / (3x - 2) be simplified to 2x - 3?

    I assume your doing GCSE so i'll try keep it straight forward:

    Basically, when dividing, your trying to see how much of the denominator (Bottom part) can fit into the numerator (top part), so you have to ask yourself, how many "3x -2"'s fit into 6? Well as 3 and 2 share no other factors other than one, you cannot simplify the bottom - and as you don't have a value for x, you are unaware of how many "3x -2"'s fit into 6.

    Let's say for example, it was "3x-3" as the denominator - well you know you have a factor of 3 in there, which simplifies to 3(x-1) (If you expand these brackets you get "3x-3" and so if you had "6 / (3(x-1))" 6/3 would become 2/1 (3 fits in 6, 2 whole times) thus making the whole fraction, 2/(x-1)
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