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Provided that x- 2 is not zero:

2x3 + x2 - 13x + 6 = 2x3 - 4x2 + 5x2 - 10x - 3x + 6

= 2x2*(x - 2) + 5x*(x - 2) - 3*(x - 2)

= (x - 2)*(2x2 + 5x - 3)

Therefore,

(2x3 + x2 - 13x + 6)/(x - 2) = (x - 2)*(2x2 + 5x - 3)/(x - 2) = 2x2 + 5x - 3

If x = 2 so that x - 2 = 0, then the expression is not defined.

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