SOLUTION: Simplify ((x^2-16)/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))

Algebra ->  Functions -> SOLUTION: Simplify ((x^2-16)/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))      Log On


   

Question 706843: Simplify

((x^2-16)/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-16%29%2F%28x%5E2%2B5x%2B6%29%29%28%28x%5E2%2B5x%2B4%29%2F%28x%5E2-2x-8%29%29 Start with the given expression.


Factor x%5E2-16 to get %28x-4%29%2A%28x%2B4%29.


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


Factor x%5E2%2B5x%2B4 to get %28x%2B4%29%2A%28x%2B1%29.


Factor x%5E2-2x-8 to get %28x%2B2%29%2A%28x-4%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28x%2B4%29%28x%2B4%29%28x%2B1%29%29%2F%28%28x%2B3%29%28x%2B2%29%28x%2B2%29%29 Simplify.


So %28%28x%5E2-16%29%2F%28x%5E2%2B5x%2B6%29%29%28%28x%5E2%2B5x%2B4%29%2F%28x%5E2-2x-8%29%29 simplifies to %28%28x%2B4%29%28x%2B4%29%28x%2B1%29%29%2F%28%28x%2B3%29%28x%2B2%29%28x%2B2%29%29.


In other words,