[tex]\bf \cfrac{3}{x-2}+\cfrac{4}{x-1}-\cfrac{1}{x}[/tex] so, no breaks on the denominator thus, the LCD will be all three then.
[tex]\bf \cfrac{3}{x-2}+\cfrac{4}{x-1}-\cfrac{1}{x}\implies \cfrac{[3x(x-1)]+[4x(x-2)]-[(x-2)(x-1)]}{x(x-2)(x-1)}
\\\\\\
\cfrac{[3x^2-3x]+[4x^2-8x]-[x^2-3x+2]}{x(x-2)(x-1)}
\\\\\\
\cfrac{3x^2-3x+4x^2-8x-x^2+3x-2}{x(x-2)(x-1)}
\\\\\\
\cfrac{6x^2-8x-2}{x(x-2)(x-1)}\implies \cfrac{2(x^2-4x-1)}{x(x-2)(x-1)}[/tex]
