SOLUTION: simplify 2x/x^2-9 + 3x/x^2+4x+3

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Question 169802: simplify
2x/x^2-9 + 3x/x^2+4x+3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%29%2F%28x%5E2-9%29+%2B+%283x%29%2F%28x%5E2%2B4x%2B3%29 Start with the given expression


%282x%29%2F%28%28x-3%29%28x%2B3%29%29+%2B+%283x%29%2F%28%28x%2B1%29%28x%2B3%29%29 Factor the denominators


Take note that the LCD is %28x-3%29%28x%2B3%29%28x%2B1%29


Multiply the first fraction by %28x%2B1%29%2F%28x%2B1%29 to get the denominator of the first fraction to the LCD



Multiply the second fraction by %28x-3%29%2F%28x-3%29 to get the denominator of the first fraction to the LCD


Distribute


%282x%5E2%2B2x%2B3x%5E2-9x%29%2F%28%28x-3%29%28x%2B3%29%28x%2B1%29%29 Combine the fractions


%285x%5E2-7x%29%2F%28%28x-3%29%28x%2B3%29%28x%2B1%29%29 Combine like terms.


%285x%5E2-7x%29%2F%28%28x%5E2-9%29%28x%2B1%29%29 FOIL %28x-3%29%28x%2B3%29 to get x%5E2-9


%285x%5E2-7x%29%2F%28x%5E3%2Bx%5E2-9x-9%29 FOIL x%5E3%2Bx%5E2-9x-9 to get x%5E3%2Bx%5E2-9x-9



So %282x%29%2F%28x%5E2-9%29+%2B+%283x%29%2F%28x%5E2%2B4x%2B3%29 simplifies to %285x%5E2-7x%29%2F%28x%5E3%2Bx%5E2-9x-9%29