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(x±a)(x±b) = x²±(a+b)x+ab.

Solve the fol...

Question

Solve the following inequality:
$\frac{x^{2} - 3 x + 24}{x^{2} - 3 x + 3} < 4$

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Solution

$\frac{x^{2} - 3 x + 24}{x^{2} - 3 x + 3} < 4$
$x^{2} - 3 x + 24 < 4 x^{2} - 12 x + 12$
$3 x^{2} - 9 x - 12 > 0$
$x^{2} - 3 x - 4 > 0$
$(x - 4) (x + 1) > 0$
$x ϵ (- \infty, - 1) \cup (4, \infty)$

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(x±a)(x±b) = x²±(a+b)x+ab.

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