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Inequalities Involving Modulus Function

Solve the fol...

Question

Solve the following inequality:
$\frac{x^{2} - 6 x + 9}{5 - 4 x - x^{2}} ⩾ 0$

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Solution

$\frac{x^{2} - 6 x + 9}{5 - 4 x - x^{2}} \geq 0$
$\frac{(x - 3)^{2}}{x^{2} + 4 x - 5} \leq 0$
$\frac{(x - 3)^{2}}{(x + 5) (x - 1)} \leq 0$
$x ϵ (- \infty, - 5) \cup (1, \infty)$

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Inequalities Involving Modulus Function

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