SOLUTION: Help with this complex rational expression with polynomials. I need to know step by step how to solve this, I keep comin up with x-1/(x+2)(x-2)+(x+2) The correct answer is 1/x+2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Help with this complex rational expression with polynomials. I need to know step by step how to solve this, I keep comin up with x-1/(x+2)(x-2)+(x+2) The correct answer is 1/x+2      Log On


   

Question 524290: Help with this complex rational expression with polynomials. I need to know step by step how to solve this, I keep comin up with x-1/(x+2)(x-2)+(x+2)
The correct answer is 1/x+2
I labeled the all over line. The denominator is 1+ 1/x-2 just to clarify.
The problem is:
x-1
_____
x^2-4
_________ <--- this is "all over"
1+ 1/x-2

Thanks for any help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-1%29%2F%28x%5E2-4%29divided by 1%2B%281%2F%28x-2%29%29 Simplify the divisor to:
1%2B%281%2F%28x-2%29%29+=+%28%28x-2%29%2B1%29%2F%28x-2%29=%28x-1%29%2F%28x-2%29
So now you have:
%28x-1%29%2F%28x%5E2-4%29divided by%28x-1%29%2F%28x-2%29 which is:
%28%28x-1%29%2F%28x%5E2-4%29%29%2A%28%28x-2%29%2F%28x-1%29%29 Factor the denominator of the first fraction:
Cancel the indicated factors to leave:
highlight%281%2F%28x%2B2%29%29