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Algebra Difficulty 2.9 Junior Find the answer

The solution set of the inequality x2x6x1>0\dfrac {x^{2}-x-6}{x-1} > 0 is ()(\quad)
A: {xx3}\{x|x 3\}
B: {xx3}\{x|x 3\}
D: {x2<x<1}\{x|-2 < x < 1\}, or 1<x<3}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: x2x6x1>0(x3)(x+2)(x1)>0(x3)(x+2)(x1)>0\dfrac {x^{2}-x-6}{x-1} > 0 \Leftrightarrow \dfrac {(x-3)(x+2)}{(x-1)} > 0 \Leftrightarrow (x-3)(x+2)(x-1) > 0
By using the method of interval testing, we find that 23-2 3,
Therefore, the correct choice is: C\boxed{C}.
To solve f(x)g(x)>0\dfrac {f(x)}{g(x)} > 0, it can be transformed into f(x)g(x)>0f(x) \cdot 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. Statement and solution reproduced as published; topic and difficulty added by this site.