Long-answer type questions (L.A.)
`(1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)(xne1,2,3,4)`

Explanation

`(1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)(xne1,2,3,4)`
or, `((1)/(x-2)-(1)/(x-1))+((1)/(x-3)-(1)/(x-2))+((1)/(x-4)-(1)/(x-3))=(1)/(6)`
or, `(1)/(x-4)-(1)/(x-1)=(1)/(6)" "or,(x-1-x+4)/((x-4)(x-1))=(1)/(6)`
or, `(3)/(x^(2)-4x-x+4)=(1)/(6)" "or,(3)/(x^(2)-5x+4)=(1)/(6)`
or, `x^(2)-5x+4=18" "or,x^(2)-5x+4-18=0`
or, `x^(2)-5x-14=0" "or,x^(2)-(7-2)x-14=0`
or, `x^(2)-7x+3x-14=0" "or,x(x-7)+2(x-7)=0`
or, (x-7)(x+2)=0
`:.` either x-7=0" "or,x+2=0
`impliesx=7" "impliesx=-2`
Hence the required equations are x=7 and x=-2.