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

Question 622641: Please help! Divide.

Found 2 solutions by lwsshak3, bucky:
Answer by lwsshak3(11628) (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) (Show Source): You can put this solution on YOUR website!
Given to divide:
.

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Note that this is one great big fraction. The numerator is:
.

.
and the denominator is:
.

.
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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Now multiply that inverted fraction times the numerator and you have:
.

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Note that the denominator of the first fraction is and it will divide into the numerator of the second fraction to give just 2. This reduces the problem to:
.

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Next note that the denominator of the second fraction can be factored by 9 to give:
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Then the numerator of the first fraction can be factored by 3 to result in:
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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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which after multiplication gives:
.

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and 6 divided by 9 is equal to
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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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