Question

Solve the following inequalities.
$\frac{x}{x+6}<\frac{1}{x}$

Answer 1

$\frac{x}{x+6}<\frac{1}{x}$

Here, $x\ne -6,0$

Now,$x^2<x+6$

$⟹x^2-x-6<0$

$⟹(x-3)(x+2)<0$

$⟹-2<x<3$

But, $x\ne 0$

Hence, solution set is $x\in (-2,3)-\left\{0\right\}$