SOLUTION: can you please help me with: (((n(3)-27 over n-3)))

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Question 152643This question is from textbook Algebra structure and method book 1
: can you please help me with: (((n(3)-27 over n-3))) This question is from textbook Algebra structure and method book 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First factor n%5E3-27


n%5E3-27 Start with the numerator.


%28n%29%5E3-%283%29%5E3 Rewrite n%5E3 as %28n%29%5E3. Rewrite 27 as %283%29%5E3.


%28n-3%29%28%28n%29%5E2%2B%28n%29%283%29%2B%283%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28n-3%29%28n%5E2%2B3n%2B9%29 Multiply


So n%5E3-27 factors to %28n-3%29%28n%5E2%2B3n%2B9%29.

In other words, n%5E3-27=%28n-3%29%28n%5E2%2B3n%2B9%29


So %28n%5E3-27%29%2F%28n-3%29 transforms into %28%28n-3%29%28n%5E2%2B3n%2B9%29%29%2F%28n-3%29


%28%28n-3%29%28n%5E2%2B3n%2B9%29%29%2F%28n-3%29 Start with the given expression.


%28highlight%28%28n-3%29%29%28n%5E2%2B3n%2B9%29%29%2Fhighlight%28%28n-3%29%29 Highlight the common terms.


%28cross%28%28n-3%29%29%28n%5E2%2B3n%2B9%29%29%2Fcross%28%28n-3%29%29 Cancel out the common terms.


n%5E2%2B3n%2B9 Simplify


So %28n%5E3-27%29%2F%28n-3%29 simplifies to n%5E2%2B3n%2B9


In other words, %28n%5E3-27%29%2F%28n-3%29=n%5E2%2B3n%2B9 where x%3C%3E3