SOLUTION: Please help me with the following problem. I need to express the following rational expression in lowest terms: 3x^2+18x-48 ----------- 2x+16

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me with the following problem. I need to express the following rational expression in lowest terms: 3x^2+18x-48 ----------- 2x+16      Log On


   

Question 195819: Please help me with the following problem. I need to express the following rational expression in lowest terms:
3x^2+18x-48
-----------
2x+16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E2%2B18x-48%29%2F%282x%2B16%29 Start with the given expression.


%283%28x%2B8%29%28x-2%29%29%2F%282x%2B16%29 Factor 3x%5E2%2B18x-48 to get 3%28x%2B8%29%28x-2%29.


%283%28x%2B8%29%28x-2%29%29%2F%282%28x%2B8%29%29 Factor 2x%2B16 to get 2%28x%2B8%29.


%283%2Ahighlight%28%28x%2B8%29%29%28x-2%29%29%2F%282%2Ahighlight%28%28x%2B8%29%29%29 Highlight the common terms.


%283%2Across%28%28x%2B8%29%29%28x-2%29%29%2F%282%2Across%28%28x%2B8%29%29%29 Cancel out the common terms.


%283%28x-2%29%29%2F%282%29 Simplify.


%283x-6%29%2F2 Distribute.


So %283x%5E2%2B18x-48%29%2F%282x%2B16%29 simplifies to %283x-6%29%2F2.


In other words, %283x%5E2%2B18x-48%29%2F%282x%2B16%29=%283x-6%29%2F2 where x%3C%3E-8