SOLUTION: 4+ 12/2x-3 divided by 5+ 15/2x-3

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Question 203294: 4+ 12/2x-3 divided by 5+ 15/2x-3
Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
Here is how I read your question.....

%284+%2B+12%29%2F%282x+-+3%29
_______________________
%285+%2B+15%29%2F%282x+-+3%29

(I am sorry I can't make that look better - I'm still learning how to set up problems here).

So anyway, when you divide with fractions, you multiply by the reciprocal. For example: %281%2F2%29%2F%282%2F3%29 is %281%2F2%29*%283%2F2%29 which is: 3%2F4. Do you remember that's how you handle division with fractions? Well, that same principle works whether you are using small fractions (like the previous example) or larger fractions, like your math problem here.

SO keeping that principle in mind, think of this......


%284+%2B+12%29%2F%282x+-+3%29
_______________________
%285+%2B+15%29%2F%282x+-+3%29


becomes.........

%284+%2B+12%29%2F%282x+-+3%29 * %282x+-+3%29%2F%285+%2B+15%29


What we do now is cancel out some factors. Can you see that the (2x - 3) in the numerator cancels the (2x - 3) in the denominator? Does that makes sense?


That leaves:

%284+%2B+12%29%2F%285+%2B+15%29 which is:
16%2F20 which reduces to:
4%2F5

I hope this helps you. :-)