SOLUTION: How do you simplify a rational problem like this: 2x^2+6x+4/4x^2-12x-16, whats the answer for this problem?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you simplify a rational problem like this: 2x^2+6x+4/4x^2-12x-16, whats the answer for this problem?       Log On


   

Question 152263: How do you simplify a rational problem like this: 2x^2+6x+4/4x^2-12x-16, whats the answer for this problem?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%5E2%2B6x%2B4%29%2F%284x%5E2-12x-16%29 Start with the given expression.


%282%2A%28x%2B2%29%2A%28x%2B1%29%29%2F%284x%5E2-12x-16%29 Factor 2x%5E2%2B6x%2B4 to get 2%2A%28x%2B2%29%2A%28x%2B1%29.


%282%2A%28x%2B2%29%2A%28x%2B1%29%29%2F%282%2A2%2A%28x%2B1%29%2A%28x-4%29%29 Factor 4x%5E2-12x-16 to get 4%2A%28x%2B1%29%2A%28x-4%29=2%2A2%28x%2B1%29%2A%28x-4%29.


Highlight the common terms.


Cancel out the common terms.


%28x%2B2%29%2F%282%28x-4%29%29 Simplify.


%28x%2B2%29%2F%282x-8%29 Distribute.


So %282x%5E2%2B6x%2B4%29%2F%284x%5E2-12x-16%29 simplifies to %28x%2B2%29%2F%282x-8%29.


In other words, %282x%5E2%2B6x%2B4%29%2F%284x%5E2-12x-16%29=%28x%2B2%29%2F%282x-8%29 where x%3C%3E-1 or x%3C%3E4