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1/(x-2)+2/(x-1)=6/x
1(x-1)x+2(x-2)x=6(x-2)(x-1)
x^2-x+2x^2-4x=6(x^2-x-2x+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 or x-3=0
x=4/3 or x=3
Therefor, x=3 or 4/3