SOLUTION: x^2-4 ------ x^2+6x+9 times x^2-9 -------- x^2+4x+4 i need to simplify this and find the restrictions. thank you so much for your help

Algebra ->  Rational-functions -> SOLUTION: x^2-4 ------ x^2+6x+9 times x^2-9 -------- x^2+4x+4 i need to simplify this and find the restrictions. thank you so much for your help      Log On


   

Question 178863: x^2-4
------
x^2+6x+9
times

x^2-9
--------
x^2+4x+4
i need to simplify this and find the restrictions.
thank you so much for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-4%29%2F%28x%5E2%2B6x%2B9%29%29%28%28x%5E2-9%29%2F%28x%5E2%2B4x%2B4%29%29 Start with the given expression.


Factor x%5E2-4 to get %28x-2%29%28x%2B2%29.


Factor x%5E2%2B6x%2B9 to get %28x%2B3%29%28x%2B3%29.


Factor x%5E2-9 to get %28x-3%29%28x%2B3%29.


Factor x%5E2%2B4x%2B4 to get %28x%2B2%29%28x%2B2%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28x-2%29%28x-3%29%29%2F%28%28x%2B3%29%28x%2B2%29%29 Simplify.


%28x%5E2-5x%2B6%29%2F%28x%5E2%2B5x%2B6%29 FOIL


So %28%28x%5E2-4%29%2F%28x%5E2%2B6x%2B9%29%29%28%28x%5E2-9%29%2F%28x%5E2%2B4x%2B4%29%29 simplifies to %28x%5E2-5x%2B6%29%2F%28x%5E2%2B5x%2B6%29.


In other words, where x%3C%3E-3 or x%3C%3E-2 (these are the restricted values)