SOLUTION: Please help! Divide. {{{ ((3y+12)/(8y^3))/((9y+36)/(16y^3)) }}}

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Question 622641: Please help! Divide.
+%28%283y%2B12%29%2F%288y%5E3%29%29%2F%28%289y%2B36%29%2F%2816y%5E3%29%29+
Found 2 solutions by lwsshak3, bucky:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
((3y+12)/(8y^3))/((9y+36)/(16y^3))
=2(3y+12)/(9y+36)
=2*3(y+4)/9(y+4)
=6/9
=2/3

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to divide:
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+%28%283y%2B12%29%2F%288y%5E3%29%29%2F%28%289y%2B36%29%2F%2816y%5E3%29%29+
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Note that this is one great big fraction. The numerator is:
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+%28%283y%2B12%29%2F%288y%5E3%29%29
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and the denominator is:
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%28%289y%2B36%29%2F%2816y%5E3%29%29+
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So you are dividing the numerator by the denominator. Remember the rule for dividing by a fraction ... namely that you can divide by a fraction by inverting the fractional divisor and then multiplying that inverted fraction by the number you are dividing into.
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When you invert the denominator you get:
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%28%2816y%5E3%29%2F%289y+%2B+36%29%29+
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Now multiply that inverted fraction times the numerator and you have:
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%28%283y%2B12%29%2F%288y%5E3%29%29%2A%28%2816y%5E3%29%2F%289y+%2B+36%29%29+
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Note that the denominator of the first fraction is 8y%5E3 and it will divide into the numerator of the second fraction 16y%5E3 to give just 2. This reduces the problem to:
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%28%283y%2B12%29%2F1%29%2A%28%282%29%2F%289y+%2B+36%29%29+
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Next note that the denominator of the second fraction can be factored by 9 to give:
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%28%283y%2B12%29%2F1%29%2A%282%2F%289%28y+%2B+4%29%29%29+
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Then the numerator of the first fraction can be factored by 3 to result in:
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%28%283%28y%2B4%29%29%2F%281%29%29%2A%28%282%29%2F%289%28y+%2B+4%29%29%29+
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So you have a (y+4) factor in the numerator and a (y+4) factor in the denominator. These cancel out and you are left with:
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%283%2F1%29%2A%282%2F9%29
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which after multiplication gives:
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%283%2A2%29%2F9+=+6%2F9
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and 6 divided by 9 is equal to 2%2F3
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and that is the answer to this problem.
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I hope this helps you to see your way through this problem
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