plz find the value of x
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[1/(x-2) - 1/(x-1)] + [1/(x-3) - 1/(x-2)] + [1/(x-4) - 1/(x-3)] =1/6,
then it will becomes
1/(x-4) - 1/(x-1) =1/6,
(x-1-x+4)/[(x-1)(x-4)] =1/6,
3/(x²-5x+4) =1/6,
18=x²-5x+4,
then
x²-5x+4-18=0,
x²-5x-14=0,
x²-(7-2)x+14=0,
x²-7x+2x+14=0,
x(x-7)-2(x-7)=0,
(x-7)(x-2)=0,
therefore
x=2 and 7
then it will becomes
1/(x-4) - 1/(x-1) =1/6,
(x-1-x+4)/[(x-1)(x-4)] =1/6,
3/(x²-5x+4) =1/6,
18=x²-5x+4,
then
x²-5x+4-18=0,
x²-5x-14=0,
x²-(7-2)x+14=0,
x²-7x+2x+14=0,
x(x-7)-2(x-7)=0,
(x-7)(x-2)=0,
therefore
x=2 and 7
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