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Chain Rule of Differentiation

Solve the fol...

Question

Solve the following inequality:
$\frac{3 x - 5}{x^{2} + 4 x - 5} > \frac{1}{2}$

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Solution

$\frac{3 x - 5}{x^{2} + 4 x - 5} > \frac{1}{2} \frac{3 x - 5}{x^{2} + 4 x - 5} - \frac{1}{2} > 0 \frac{6 x - 10 - x^{2} - 4 x + 5}{{2 (x}^{2} + 4 x - 5)} > 0 \frac{x^{2} - 2 x + 5}{2 (x^{2} + 4 x - 5)} < 0$
discriminant of
$x^{2} - 2 x + 5 < 0 f o r \forall x \in R x^{2} - 2 x + 5 > 0 \forall x \in R \frac{1}{x^{2} + 4 x - 5} < 0 \frac{1}{(x + 5) (x - 1)} < 0 x \in (- 5, 1)$

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