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Solve for x: 1/x–2+2/x–1=6/x

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Solve for x: 1/(x–2)+2/(x–1)=6/x

solve it

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1 Answer

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 1/x-2+2/x-1=6/x

1(x-1)+2(x-2)/x2-x-2x+2=6/x

x-1+2x-4/x2-3x+2=6/x

3x-5/x2-3x+2=6/x

3x2-5x=6x2-18x+12

6x2-3x2-18x+5x+12=0

3x2-13x+12 = 0

3x2-9x-4x+12 = 0

3x(x-3)-4(x-3) = 0

(3x-4)(x-3)=0

x=3 or 4/3

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