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The inequation is as following:

$$\frac{\pi x^2-(1+\pi^2)x+\pi}{-2x^2+3\pi x}\gt 0$$

So far I was able to factor the inequation, but I don't know how to proceed from now on:

$$\frac{(x-1)(x-\pi^2)}{-2x(x-\frac{3\pi}{2})}\gt 0$$

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    $\begingroup$ Make a sign chart write down areas where the function is $0$ or undefined, then fill in the signs between those points. $\endgroup$ Commented Feb 15, 2017 at 23:06

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The sign changes when the numerator goes through zero, which is at $x=1$ and $x=\pi^2$. The fraction becomes undefined when the denominator goes to zero which is at ????? The sign can only change at those points, so check in each region of $x$.

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