SOLUTION: solve for x: 2/x+4 - 1/x+3 = 1 - 2/x^2+7x+12 please help homework for tomorrow

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Question 979580: solve for x:
2/x+4 - 1/x+3 = 1 - 2/x^2+7x+12
please help homework for tomorrow

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve for x:
2/x+4 - 1/x+3 = 1 - 2/x^2+7x+12
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Find a common denominator.
x^2+7x+12 = (x+4)*(x+3) so that will work.
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2(x+3)/DEN - (x+4)/DEN = (x^2+7x+12 - 2)/DEN
Multiply thru by the DEN
2x+6 -x-4 = x^2+7x+10
x+2 = x^2+7x+10
x^2 + 6x + 8 = 0
(x+2)*(x+4) = 0
x = -2
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x = -4
*********** x=-4 make the DEN of the 1st term zero, so it's not allowed.