Question 643834
x/(2x+2)=-2x/(4x+4)+(2x-3)/(x-4) 
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Factor:
x/(2(x+1)) = -2x/(4(x+1) + (2x-3)/(x-4)
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Multiply thru by lcm = 4(x+1)(x-4)
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2x(x-4) = (-2x)(x-4) + (2x-3)(4(x+1))
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2x^2-8x = -2x^2+8x + 4(2x^2-x-3)
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4x^2-16x = 8x^2-4x - 12
4x^2 + 12x -12 = 0
x^2 + 3x - 3 = 0
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x = [-3 +- sqrt(9+12)]/2
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x = [-3+sqrt(21)]/2 or x = [-3-sqrt(21)]/2
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Cheers,
Stan H.