SOLUTION: b^2-9/b^3-27 i know i have to use the cube root but i stilll dont get how this problem is sloved.. can you please explain this (:

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: b^2-9/b^3-27 i know i have to use the cube root but i stilll dont get how this problem is sloved.. can you please explain this (:      Log On

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Question 199584: b^2-9/b^3-27
i know i have to use the cube root but i stilll dont get how this problem is sloved.. can you please explain this (:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%28b%5E2-9%29%2F%28b%5E3-27%29 Start with the given expression.


%28%28b-3%29%2A%28b%2B3%29%29%2F%28b%5E3-27%29 Factor b%5E2-9 to get %28b-3%29%28b%2B3%29 (use the difference of squares formula)


%28%28b-3%29%2A%28b%2B3%29%29%2F%28%28b-3%29%2A%28b%5E2%2B3%2Ab%2B9%29%29 Factor b%5E3-27 to get %28b-3%29%28b%5E2%2B3b%2B9%29 (use the difference of cubes formula)


%28highlight%28%28b-3%29%29%28b%2B3%29%29%2F%28highlight%28%28b-3%29%29%28b%5E2%2B3b%2B9%29%29 Highlight the common terms.


%28cross%28%28b-3%29%29%28b%2B3%29%29%2F%28cross%28%28b-3%29%29%28b%5E2%2B3b%2B9%29%29 Cancel out the common terms.


%28b%2B3%29%2F%28b%5E2%2B3b%2B9%29 Simplify.


So %28b%5E2-9%29%2F%28b%5E3-27%29 simplifies to %28b%2B3%29%2F%28b%5E2%2B3b%2B9%29.


In other words, %28b%5E2-9%29%2F%28b%5E3-27%29=%28b%2B3%29%2F%28b%5E2%2B3b%2B9%29 where b%3C%3E3