1/(x-1)(x-2) + 1/(x-2)(x-3) + 1/(x-3)(x-4) = 1/6

Asked by  | 2nd Oct, 2008, 11:49: AM

Expert Answer:

we can split the terms as shown below

1/(x-1)(x-2) = 1/(x-2)  - 1/(x-1)

1/(x-2)(x-3) = 1/(x-3)  - 1/(x-2)

1/(x-3)(x-4) = 1/(x-4)  - 1/(x-3)

now LHS = 1/(x-4)- 1/(x-1) = 3 /(x-1)(x-4) = 1/6

so x2 - 5x + 4 =18

x2 -5x -14 =0

(x-7) (x+2) =0

x=7 or x=-2

Answered by  | 30th Nov, 2008, 02:49: AM

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