SOLUTION: SOLVE : 4\X-3 + 2X\X-3 = 12\X^2-6X+9

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Question 283698: SOLVE :
4\X-3 + 2X\X-3 = 12\X^2-6X+9
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
SOLVE :
4\X-3 + 2X\X-3 = 12\X^2-6X+9
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Multiply thru by x^2-6x+9 = (x-3)^2
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4(x-3) + 2x(x-3) = 12
4x-12 + 2x^2-6x = 12
2x^2 -2x -24 = 0
x^2 -x - 12 = 0
(x-4)(x+3) = 0
x = 4 or x = -3
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Cheers,
Stan H.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4\X-3 + 2X\X-3 = 12\X^2-6X+9
4/ x-3 +2x/ x-3 = 12 / ( x-3)^2
(x-3 ) is a common factor in all the terms and on both sides of the equation
4+2x=12*(x-3) /(x-3)^2
4+2x= 12 / x-3
(4+2x)(x-3)=12
4x-12+2x^2-6x=12
2x^2-2x-24=0
x^2-x-12=0
x^2-4x+3x-12=0
x(x-4)+3(x-4)=0
(x-4)(x+3)=0