SOLUTION: We are working on rational expressions. I can not seem to get the jist of building rational expressions to higher terms. Example, I know that if x +3 was mulitiplied by x^2 + 3^2 t

Algebra ->  Rational-functions -> SOLUTION: We are working on rational expressions. I can not seem to get the jist of building rational expressions to higher terms. Example, I know that if x +3 was mulitiplied by x^2 + 3^2 t      Log On


   

Question 218381: We are working on rational expressions. I can not seem to get the jist of building rational expressions to higher terms. Example, I know that if x +3 was mulitiplied by x^2 + 3^2 the result would be x^3 + 27. That's easy enough, but I have problems writing that in correctly factored form. Any hints on how I can get better at this? Example/Question: How would I correctly write 12/x +3 = ?/ x^3 + 27? Thanks for your assistance, tips and suggestions.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Watch out
%28x%2B3%29%28x%5E2%2B9%29+ does NOT equal x%5E3%2B27
%28x%2B3%29%28x%5E2%2B9%29+
x%28x%5E2%2B9%29+%2B+3%28x%5E2%2B9%29
x%5E3+%2B+9x+%2B+3x%5E2+%2B+27
x%5E3+%2B+3x%5E2+%2B9x+%2B+27
Now that you see that. can you do the second one yourself?

12%2F%28x+%2B3%29+=+x%2F+%28x%5E3+%2B+27%29
The factorization of sum to cubes is given here --> http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Sum-or-Difference-of-Cubes.topicArticleId-38949,articleId-38892.html