SOLUTION: Multiply and, if possible, simplify. (2x + 2) (3x^2 + 12x + 12) ______ * ___________ _______ (x + 2) (x^2 - 1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Multiply and, if possible, simplify. (2x + 2) (3x^2 + 12x + 12) ______ * ___________ _______ (x + 2) (x^2 - 1)      Log On


   

Question 283861: Multiply and, if possible, simplify.
(2x + 2) (3x^2 + 12x + 12)
______ * ___________________
(x + 2) (x^2 - 1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%2B2%29%2F%28x%2B2%29%29%28%283x%5E2%2B12x%2B12%29%2F%28x%5E2-1%29%29 Start with the given expression.


%28%282%28x%2B1%29%29%2F%28x%2B2%29%29%28%283x%5E2%2B12x%2B12%29%2F%28x%5E2-1%29%29 Factor the first numerator.


%28%282%28x%2B1%29%29%2F%28x%2B2%29%29%28%283%28x%2B2%29%28x%2B2%29%29%2F%28x%5E2-1%29%29 Factor the second numerator.


Factor the second denominator.


%282%2A3%28x%2B1%29%28x%2B2%29%28x%2B2%29%29%2F%28%28x%2B2%29%28x%2B1%29%28x-1%29%29 Combine the fractions.


Highlight the common terms.



Cancel out the common terms.


%282%2A3%28x%2B2%29%29%2F%28x-1%29 Simplify.


%286%28x%2B2%29%29%2F%28x-1%29 Multiply.


%286x%2B12%29%2F%28x-1%29 Distribute.


So %28%282x%2B2%29%2F%28x%2B2%29%29%28%283x%5E2%2B12x%2B12%29%2F%28x%5E2-1%29%29 simplifies to %286x%2B12%29%2F%28x-1%29


In other words, where x%3C%3E-2, x%3C%3E-1 or x%3C%3E1