SOLUTION: I need help simplifying this problem: x^2-2x-8 __________ 4-x

Algebra ->  Exponents -> SOLUTION: I need help simplifying this problem: x^2-2x-8 __________ 4-x      Log On


   

Question 234576: I need help simplifying this problem:
x^2-2x-8
__________
4-x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To reduce any fraction you have to have common factors to cancel. To have common factors, you have to have the numerator and denominator factored. So this is where we will start.

The numerator is a trinomial which will factor. The denominator will not factor unless we factor out a 1:
%28%28x%2B2%29%28x-4%29%29%2F%281%284-x%29%29
At first glance it may not seem that we have any common factors to cancel. However, x-4 and 4-x are negatives of each other. So it we factor out a -1 from either the numerator or the denominator then we will have factors to cancel:
%28%28x%2B2%29%28x-4%29%29%2F%28-1%28x-4%29%29
Now we can cancel the (x-4)'s:
%28%28x%2B2%29cross%28%28x-4%29%29%29%2F%28-1cross%28%28x-4%29%29%29
leaving:
%28x%2B2%29%2F%28-1%29
which simplifies to
-x+-+2

So keep an eye out for factors that are negatives of each other. Factoring out a -1 from one of them will make them match.