Question

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

Answer 1

Answer:

x = 7 or x =-2

Explanation:

i )1/(x-1)(x-2)

= 1/(x-2) - 1/(x-1) ----(1)

ii )1/(x-2)(x-3)

= 1/(x-3) - 1/(x-2)----(2)

iii) 1/(x-3)(x-4)

= 1/(x-4)-1/(x-3) ---( 3)

Now ,

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

=> 1/(x-2) -1/(x-1) +1/(x-3)

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

=> 1/(x-4) -1/(x-1) = 1/6

=> [(x-1)-(x-4)]/[(x-4)(x-1)]=1/6

=> 3/(x²-5x+4) = 1/6

=> 18 = x²-5x+4

=> x²-5x+4-18=0

=> x²-5x-14=0

=> x² -7x+2x-14=0

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

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

=> x-7 = 0 or x+2 = 0

=> x = 7 or x = -2

Therefore,

x = 7 or x = -2

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