1/x-2+2/x-1=6/x solve
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1/x-2+2/x-1=6/x
1(x-1)+2(x-2)/(x-2)(x-1)=6/x
x-1+2x-4/x^2-x-2x+2=6/x
3x-5/x^2-3x+2=6/x
Cross multiply
X(3x-5)=6(x^2-3x+2)
3x^2-5x=6x^2-18x+12
6x^2-3x^2-18x+5x+12=0
3x^2-13x+12=0
3x^2-9x-4x+12=0
3x(x-3)-4(x-3)=0
(3x-4)(x-3)=0
3x-4=0
3x=4
X=4/3
x-3=0
x=3
therefor, x=3 or 4/3
1(x-1)+2(x-2)/(x-2)(x-1)=6/x
x-1+2x-4/x^2-x-2x+2=6/x
3x-5/x^2-3x+2=6/x
Cross multiply
X(3x-5)=6(x^2-3x+2)
3x^2-5x=6x^2-18x+12
6x^2-3x^2-18x+5x+12=0
3x^2-13x+12=0
3x^2-9x-4x+12=0
3x(x-3)-4(x-3)=0
(3x-4)(x-3)=0
3x-4=0
3x=4
X=4/3
x-3=0
x=3
therefor, x=3 or 4/3
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