SOLUTION: Please help me work this problem. I really need to understand... 2x/x^2-9 + 3x/x^2+4x+3 Thank you in advance for your help!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me work this problem. I really need to understand... 2x/x^2-9 + 3x/x^2+4x+3 Thank you in advance for your help!      Log On


   

Question 329548: Please help me work this problem. I really need to understand...
2x/x^2-9 + 3x/x^2+4x+3
Thank you in advance for your help!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%29%2F%28x%5E2-9%29 + %283x%29%2F%28x%5E2%2B4x%2B3%29
:
We can factor both denominators (the 1st one is the "difference of squares")
%282x%29%2F%28%28x-3%29%28x%2B3%29%29 + %283x%29%2F%28%28x%2B3%29%28x%2B1%29%29
:
The common denominator is (x-3)(x+3)(x+1)
%282x%28x%2B1%29+%2B+3x%28x-3%29%29%2F%28%28x-3%29%28x%2B3%29%28x%2B1%29%29
:
Multiply inside the brackets
%282x%5E2+%2B+2x+%2B+3x%5E2+-+9x%29%2F%28%28x-3%29%28x%2B3%29%28x%2B1%29%29
:
Combine like terms in the numerator
%285x%5E2+-+7x%29%2F%28%28x-3%29%28x%2B3%29%28x%2B1%29%29 = %28x%285x+-+7%29%29%2F%28%28x-3%29%28x%2B3%29%28x%2B1%29%29