SOLUTION: I need help multiplying this rational expression. x+9/x-3 * x^3-27/x^2+3x+9

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help multiplying this rational expression. x+9/x-3 * x^3-27/x^2+3x+9      Log On


   

Question 194479: I need help multiplying this rational expression. x+9/x-3 * x^3-27/x^2+3x+9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%2B9%29%2F%28x-3%29%29%28%28x%5E3-27%29%2F%28x%5E2%2B3x%2B9%29%29 Start with the given expression.


Factor x%5E3-27 to get %28x-3%29%2A%28x%5E2%2B3%2Ax%2B9%29. Note: use the difference of cubes formula.


%28%28x%2B9%29%28x-3%29%28x%5E2%2B3x%2B9%29%29%2F%28%28x-3%29%28x%5E2%2B3x%2B9%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


x%2B9 Simplify.


So %28%28x%2B9%29%2F%28x-3%29%29%28%28x%5E3-27%29%2F%28x%5E2%2B3x%2B9%29%29 simplifies to x%2B9.


In other words, %28%28x%2B9%29%2F%28x-3%29%29%28%28x%5E3-27%29%2F%28x%5E2%2B3x%2B9%29%29=x%2B9 where x%3C%3E3