SOLUTION: Simplify x^2+5x+6/x^2-4 * x^2-5x+6/x^2-9

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify x^2+5x+6/x^2-4 * x^2-5x+6/x^2-9      Log On


   

Question 168898: Simplify x^2+5x+6/x^2-4 * x^2-5x+6/x^2-9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2%2B5x%2B6%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29 Start with the given expression.


Factor x%5E2%2B5x%2B6 to get %28x%2B3%29%2A%28x%2B2%29.


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


Factor x%5E2-5x%2B6 to get %28x-2%29%2A%28x-3%29.


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


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1 Simplify.


So %28%28x%5E2%2B5x%2B6%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29 simplifies to 1.


In other words, %28%28x%5E2%2B5x%2B6%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29=1 where x%3C%3E-3, x%3C%3E-2, x%3C%3E2, or x%3C%3E3