SOLUTION: We are currently working on rational expressions in my Intermediate Algebra class and I can't figure this problem out. I am working from the textbook, so I am able to see the corr

Question 901407: We are currently working on rational expressions in my Intermediate Algebra class and I can't figure this problem out. I am working from the textbook, so I am able to see the correct answer, but I have not been able to get my work to match the answer. So my problem is 3/(x+3) + 5/(x^2+6+9) - x/x^2-9
I have factored that out to be 3/(x+3) + 5/(x+3)(x+3)+ -x/(x+3)(x-3). After I found the LCD of "(x+3)(x+3)(x-3) I then multiplied to get "3x+9+3x-9+5x-15-x^2-3x" over (the LCD). After combing like terms I get "-x^2+8x-15". That is pretty far from the correct answer, and I'm not sure where I went wrong. If anyone can help me get this right I would be very grateful!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
3/(x+3) + 5/(x^2+6x+9) - x/(x^2-9) =
3/(x+3) + 5/(x+3)^2 - x / (x+3)(x-3) =
LCM = (x+3)^2(x-3)
3(x+3)(x-3) + 5(x-3) - x(x-3) / (x+3)^2(x-3)
cancel (x-3) from numerator and denominator
3(x+3) + 5 - x / (x+3)^2 =
3x+9 + 5 - x / (x+3)^2
2x + 14 / (x+3)^2 =
2(x+7) / (x+3)^2

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