SOLUTION: what is the quotient dē/ (d plus 4) divided by dē - 4d / (dē plus 8d plus 16)

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Question 151700: what is the quotient dē/ (d plus 4) divided by dē - 4d / (dē plus 8d plus 16)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28d%5E2%29%2F%28d%2B4%29%29%2F%28%28d%5E2-4d%29%2F%28d%5E2%2B8d%2B16%29%29 Start with the given expression.


%28%28d%5E2%29%2F%28d%2B4%29%29%28%28d%5E2%2B8d%2B16%29%2F%28d%5E2-4d%29%29 Multiply the first fraction %28d%5E2%29%2F%28d%2B4%29 by the reciprocal of the second fraction %28d%5E2-4d%29%2F%28d%5E2%2B8d%2B16%29.


%28%28d%2Ad%29%2F%28d%2B4%29%29%28%28d%5E2%2B8d%2B16%29%2F%28d%5E2-4d%29%29 Factor d%5E2 to get d%2Ad.


%28%28d%2Ad%29%2F%28d%2B4%29%29%28%28%28d%2B4%29%28d%2B4%29%29%2F%28d%5E2-4d%29%29 Factor d%5E2%2B8d%2B16 to get %28d%2B4%29%28d%2B4%29.


%28%28d%2Ad%29%2F%28d%2B4%29%29%28%28%28d%2B4%29%28d%2B4%29%29%2F%28d%2A%28d-4%29%29%29 Factor d%5E2-4d to get d%2A%28d-4%29.


%28d%2Ad%28d%2B4%29%28d%2B4%29%29%2F%28d%28d%2B4%29%28d-4%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28d%28d%2B4%29%29%2F%28d-4%29 Simplify.


%28d%5E2%2B4d%29%2F%28d-4%29 Distribute.


So %28%28d%5E2%29%2F%28d%2B4%29%29%2F%28%28d%5E2-4d%29%2F%28d%5E2%2B8d%2B16%29%29 simplifies to %28d%5E2%2B4d%29%2F%28d-4%29.


In other words, where d%3C%3E0, d%3C%3E-4, or d%3C%3E4