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Find the interval satisfied by x^2 - 8x + 12/x - 6 > 0.

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Find the interval satisfied by x2 - 8x + 12/x - 6 > 0.

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x2 - 8x + 12/x - 6 (x - 6)(x - 2)/(x - 6) = x - 2 for x ≠ 6

x2 - 8x + 12/x - 6 (x - 6) > 0

⇒ (x − 2) > 0 ⇒ x > 2

But x ≠ 6. So x ∈ (2, 6) ∪ (6, ∞).

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