Question 201334: Please help. I'm not sure I have this done correctly.
3/-5-x - x/x-3=0
Found 2 solutions by RAY100, MathTherapy:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Please review to assure correct problem
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3/(-5-x) - x/(x-3)
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just rearrange the first term, to get better den
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-3/(x+5) -x /(x-3)
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LCD = (x+5)(x-3)
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[ -3 (x-3) -x(x+5)] / (x+5)(x-3)
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[ -3x +9 -x^2 -5x ] / (x+5)(x-3)
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[ -x^2 -8x +9 ] / (x+5)(x-3)
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[ -1 ( x^2 +8x -9) ] / ( x+5)(x-3)
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[-1 (x-1)(x+9)] / [ (x+5)(x-3) ]
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checking let x=0 in original and answer,,,both = -3/5,,,,ok
doing same for x=1, both = zero,,,ok
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! 
Multiply equation by LCD (-5-x)(x-3). This gives us:
3(x-3) – x(-5-x) = 0(-5-x)(x-3) = 
= 
(x + 9)(x – 1) = 0
Therefore, x = - 9 or 1, or {- 9, 1}.
Checking, when x = - 9
= 
 = 
Multiply equation by LCD, - 12
-3(3) + 1(9), or, -9 + 9 = 0 (TRUE)
Checking, when x = 1
= 
= 
Multiply equation by LCD, - 6
1(3) – 3(1) = 0, or, 3 – 3 = 0 (TRUE)
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