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  4. The solution set of the inequation (x2+6x-7/|x+4|)<0 is

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Q. The solution set of the inequation $\frac {x^2+6x-7}{|x+4|}<0$ is

KCETKCET 2015Complex Numbers and Quadratic Equations

Solution:

$\frac{x^{2}+6x-7}{\left|x+4\right|}<0$
We know that $|x + 4| >\, 0 $
$\Rightarrow x^{2} + 6x - 7 < \,0$ and $x \ne- 4$
$\Rightarrow \left(x + 7\right)\left(x - 1\right) < \,0$ and $x \ne- 4$
$\Rightarrow x\,\in\,\left(-7,1\right)-\left\{-4\right\}$
$\Rightarrow x\,\in\,\left(-7,-4\right)\cup\left(-4, 1\right)$