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Solving Inequalities

Solve the fol...

Question

Solve the following inequality:
$\frac{x^{2} - 5 x + 7}{- 2 x^{2} + 3 x + 2} > 0$

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Solution

$\frac{x^{2} - 5 x + 7}{- 2 x^{2} + 3 x + 2} > 0$
$x^{2} - 5 x + 7$
Discriminant less than zero for all x belongs to R
$\frac{1}{- 2 x^{2} + 3 x + 2} > 0$
$\frac{1}{2 x^{2} - 3 x - 2} < 0$
$\frac{1}{2 x^{2} - 4 x + x - 2} < 0$
$\frac{1}{(2 x + 1) (x - 2)} < 0$
$x \in (\frac{- 1}{2}, 2)$

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