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Definition of Functions

Solve the fol...

Question

Solve the following inequality:
$\frac{1 + x^{2}}{x^{2} - 5 x + 6} < 0$

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Solution

$\frac{1 + x^{2}}{x^{2} - 5 x + 6} < 0$
As $1 + x^{2} > 0 \forall x ϵ R$
$\frac{1}{x^{2} - 5 x + 6} < 0$
$\frac{1}{(x - 2) (x - 3)} < 0$
$x ϵ (2, 3)$

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