SOLUTION: Hello, Please help me I need to express the following rational expression in lowest terms x^2-x-12 -------- x^2-16 Thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, Please help me I need to express the following rational expression in lowest terms x^2-x-12 -------- x^2-16 Thank you!      Log On


   

Question 196034: Hello,
Please help me I need to express the following rational expression in lowest terms
x^2-x-12
--------
x^2-16
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-x-12%29%2F%28x%5E2-16%29 Start with the given expression.


%28%28x%2B3%29%28x-4%29%29%2F%28x%5E2-16%29 Factor x%5E2-x-12 to get %28x%2B3%29%28x-4%29.


%28%28x%2B3%29%28x-4%29%29%2F%28%28x-4%29%28x%2B4%29%29 Factor x%5E2-16 to get %28x-4%29%28x%2B4%29.


%28%28x%2B3%29highlight%28%28x-4%29%29%29%2F%28highlight%28%28x-4%29%29%28x%2B4%29%29 Highlight the common terms.


%28%28x%2B3%29cross%28%28x-4%29%29%29%2F%28cross%28%28x-4%29%29%28x%2B4%29%29 Cancel out the common terms.


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


So %28x%5E2-x-12%29%2F%28x%5E2-16%29 simplifies to %28x%2B3%29%2F%28x%2B4%29.


In other words, %28x%5E2-x-12%29%2F%28x%5E2-16%29=%28x%2B3%29%2F%28x%2B4%29 where x%3C%3E-4 or x%3C%3E4