SOLUTION: SIMPLIFY the expression: (1/x^2+6x+8)−(1/x^2−2x−8) and give your answer in the form of f(x)/g(x) My solution was (1/(x-4)(x+4)), but it was incorrect.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: SIMPLIFY the expression: (1/x^2+6x+8)−(1/x^2−2x−8) and give your answer in the form of f(x)/g(x) My solution was (1/(x-4)(x+4)), but it was incorrect.       Log On


   

Question 384066: SIMPLIFY the expression:
(1/x^2+6x+8)−(1/x^2−2x−8)
and give your answer in the form of f(x)/g(x)
My solution was (1/(x-4)(x+4)), but it was incorrect.
Found 2 solutions by mananth, Theo:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F%28x%5E2%2B6x%2B8%29%29-%281%2F%28x%5E2-2x-8%29%29
...
%281%2F%28x%2B2%29%28x%2B4%29%29-%281%2F%28x-4%29%28x%2B2%29%29
...
LCD = (x+2)(x+4)(x-4)
..
%28%28x-4%29-%28x%2B4%29%29%2F%28x%2B2%29%28x%2B4%29%28x-4%29
...
%28-8%29%2F%28%28x%2B2%29%28x%2B4%29%28x-4%29%29
now write in whichever form

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The solution that I came up with is:

%28-8%29%2F%28%28x%2B2%29%2A%28x%2B4%29%2A%28x-4%29%29

I checked the solution out by assuming x was equal to 2 and solving both the original expression and the final expression.

They came out to the same answer leading to the conclusion that I simplified correctly.

My manual calculations are in the picture shown below:

***** picture not found *****

first I factored.
then I found common denominator.
then I combined numerator under same denominator.
then I performed calculations on numerator.
result was final answer.