SOLUTION: Solve for x: 1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3, x is not equal to 1,2,3

Question 1088305: Solve for x: 1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3, x is not equal to 1,2,3
Answer by natolino_2017(77) (Show Source): You can put this solution on YOUR website!
if x is not equal to 1,2,3
we can solve this equation:
(x-3) + (x-1) = 2(x-1)(x-2)(x-3)/3
6x - 12 = 2(x^3-6x^2+11x-6)
x^3-6x^2+8x = 0
x(x^2-6x+8) = 0
x(x-2)(x-4) = 0 using restriction.
answer is {0,4}.
if we put x=0 on the first equation: 1/2 + 1/6 = 2/3 (true)
if we put x=4 on the first equation: 1/6 + 1/2 = 2/3 (true).
@natolino_
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