The solution set of the inequality x−1x2−x−6>0 is () A: {x∣x3} B: {x∣x3} D: {x∣−2<x<1}, or 1<x<3}
This was a multiple-choice question, but the options didn't survive into the
source we have. The answer given is C, and the solution
below works it through.
Solution
To solve: x−1x2−x−6>0⇔(x−1)(x−3)(x+2)>0⇔(x−3)(x+2)(x−1)>0 By using the method of interval testing, we find that −23, Therefore, the correct choice is: C. To solve g(x)f(x)>0, it can be transformed into f(x)⋅g(x)>0, and then solved using the method of interval testing. This question mainly examines the methods of solving rational inequalities and polynomial inequalities, and is considered a basic question on inequalities.
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Source: NuminaMath-1.5,
licensed Apache-2.0.
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