[tex]1/((x - 1)(x - 2)) + 1/((x - 2)(x - 3)) + 1/((x - 3)(x - 4)) = 1/6[/tex]
[(x - 3)(x - 4) + (x - 1)(x - 4) + (x - 1)(x - 2)] /((x - 1)(x - 2)(x - 3)(x - 4)) = 1/6
(x^2 - 7x + 12 + x^2 - 5x + 4 + x^2 - 3x + 2)/((x - 1)(x - 2)(x - 3)(x - 4)) = 1/6
[tex](3x^2 - 15x + 18) /((x - 1)(x - 2)(x - 3)(x - 4)) = 1/6[/tex]
[tex][3(x - 3)(x - 2)] /((x - 1)(x - 2)(x - 3)(x - 4)) = 1/6[/tex]
[tex]3 /((x - 1)(x - 4)) = 1/6[/tex]
[tex]x^2 - 5x + 4 = 18[/tex]
[tex]x^2 - 5x - 14 = 0[/tex]
[tex](x + 2)(x - 7) = 0[/tex]
[tex]x = -2 , 7[/tex]
