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Chain Rule of Differentiation

Solve the fol...

Question

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

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Solution

$\frac{x^{2} - 4 x + 5}{x^{2} + 5 x + 6} \geq 0$
As discriminant of $x^{2} - 4 x + 5 < 0$ , so
$x^{2} - 4 x + 5 > 0 \forall x \in R \frac{1}{x^{2} - 5 x + 6} \geq 0 \frac{1}{(x + 2) (x + 3)} \geq 0 x \in (- \infty, - 3) \cup (- 2, \infty)$

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