SOLUTION: I need help trying to solve this. Well I know the answer, I just need a deeper explanation. x^2-x-6/x^2-4 The answer they gave was x-3/x-2

Algebra ->  Exponents -> SOLUTION: I need help trying to solve this. Well I know the answer, I just need a deeper explanation. x^2-x-6/x^2-4 The answer they gave was x-3/x-2      Log On


   

Question 624721: I need help trying to solve this. Well I know the answer, I just need a deeper explanation.
x^2-x-6/x^2-4
The answer they gave was x-3/x-2
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is to factor each piece and cancel any common factors

%28x%5E2-x-6%29%2F%28x%5E2-4%29

%28%28x-3%29%28x%2B2%29%29%2F%28x%5E2-4%29

%28%28x-3%29%28x%2B2%29%29%2F%28%28x-2%29%28x%2B2%29%29

%28%28x-3%29%2Ahighlight%28%28x%2B2%29%29%29%2F%28%28x-2%29%2Ahighlight%28%28x%2B2%29%29%29

%28%28x-3%29%2Across%28%28x%2B2%29%29%29%2F%28%28x-2%29%2Across%28%28x%2B2%29%29%29

%28x-3%29%2F%28x-2%29


So %28x%5E2-x-6%29%2F%28x%5E2-4%29 fully simplifies to %28x-3%29%2F%28x-2%29

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-x-6%29%2F%28x%5E2-4%29

The numerator x²-x-6 factors as (x-3)(x+2)

To see how to do that watch this youtube video:


http://www.youtube.com/watch?v=jR6RBA9bois&feature=relmfu

The denominator x²-4 factors as (x-2)(x+2)

To see how to do that watch this youtube video:

http://www.youtube.com/watch?v=_qyVzH3e1dY

So

%28x%5E2-x-6%29%2F%28x%5E2-4%29

becomes

%28%28x-3%29%28x%2B2%29%29%2F%28%28x-2%29%28x%2B2%29%29

Now the (x+2) on the top cancels with the (x+2)
on the bottom, like this:

%28%28x-3%29%28cross%28x%2B2%29%29%29%2F%28%28x-2%29%28cross%28x%2B2%29%29%29

And all that's left is

%28x-3%29%2F%28x-2%29

Edwin