SOLUTION: x^2+18x+81/-28x/x+9/-7x

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Question 189442: x^2+18x+81/-28x/x+9/-7x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2%2B18x%2B81%29%2F%28-28x%29%29%2F%28%28x%2B9%29%2F%28-7x%29%29 Start with the given expression.


%28%28x%5E2%2B18x%2B81%29%2F%28-28x%29%29%28%28-7x%29%2F%28x%2B9%29%29 Multiply the first fraction %28x%5E2%2B18x%2B81%29%2F%28-28x%29 by the reciprocal of the second fraction %28x%2B9%29%2F%28-7x%29.


%28%28%28x%2B9%29%28x%2B9%29%29%2F%28-28x%29%29%28%28-7x%29%2F%28x%2B9%29%29 Factor x%5E2%2B18x%2B81 to get %28x%2B9%29%28x%2B9%29.


%28%28%28x%2B9%29%28x%2B9%29%29%2F%28-7x%2A4%29%29%28%28-7x%29%2F%28x%2B9%29%29 Factor -28x to get -7%2A4x. Rearrange to get -7x%2A4


%28-7x%28x%2B9%29%28x%2B9%29%29%2F%28-7x%2A4%28x%2B9%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x%2B9%29%2F4 Simplify.


So %28%28x%5E2%2B18x%2B81%29%2F%28-28x%29%29%2F%28%28x%2B9%29%2F%28-7x%29%29 simplifies to %28x%2B9%29%2F4.


In other words, %28%28x%5E2%2B18x%2B81%29%2F%28-28x%29%29%2F%28%28x%2B9%29%2F%28-7x%29%29+=+%28x%2B9%29%2F4 where x%3C%3E-9 or x%3C%3E0