SOLUTION: Can you please help with this rational equation? It would be greatly appreciated. x/x-2=1/2-x+2/x I used the LCD, 2x(x-2) but am arriving at a quadratic equation that results

Question 311634: Can you please help with this rational equation? It would be greatly appreciated.
x/x-2=1/2-x+2/x
I used the LCD, 2x(x-2) but am arriving at a quadratic equation that results in an imaginary number, which according to my answer key is not correct. Thank you for your assistance.
Tina
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x/x-2 =1/2- x+2/x
x/x-2 +x+2 / x =1/2
LCM x(x-2)
x^2+x^2-4 /x(x-2)=1/2
2x^2+2x^2-8 =x^2-2x
3x^2+2x-8=0
3x^2 +6x-4x-8=0
3x(x+2)-4(x+2)=0
(3x-4)(x+2)=0
x=4/3 OR -2
I am not too sure I have copied the problem right
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