SOLUTION: Banging my head on desk. Please help (3x/(x^2-4)+(3+x)/(x+2) I know that the solution is x^2+4x-6/x^2-1 Have no idea how to get there. Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Banging my head on desk. Please help (3x/(x^2-4)+(3+x)/(x+2) I know that the solution is x^2+4x-6/x^2-1 Have no idea how to get there. Thank you      Log On


   

Question 222637: Banging my head on desk. Please help
(3x/(x^2-4)+(3+x)/(x+2)

I know that the solution is x^2+4x-6/x^2-1
Have no idea how to get there.
Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%29%2F%28x%5E2-4%29 + %283%2Bx%29%2F%28x%2B2%29
The first denominator is "difference of squares" factor it
%283x%29%2F%28%28x-2%29%28x%2B2%29%29 + %283%2Bx%29%2F%28x%2B2%29
We can see the common denominator is: (x-2)(x+2) so we have
%28%283x%29+%2B+%28x-2%29%283%2Bx%29%29%2F%28%28x-2%29%28x%2B2%29%29
FOIL
%28%283x%29+%2B+%283x+%2B+x%5E2+-+6+-2x%29%29%2F%28%28x-2%29%28x%2B2%29%29
group like terms and combine
%28%28x%5E2+%2B+3x+%2B+3x+-+2x+-+6%29%29%2F%28%28x-2%29%28x%2B2%29%29 = %28%28x%5E2+%2B+4x+-+6%29%29%2F%28%28x-2%29%28x%2B2%29%29
Foil the denominator to get the original denominator
%28%28x%5E2+%2B+4x+-+6%29%29%2F%28x%5E2-4%29