Question

x/x-2<0 find the value of x​

Answer 1

$\large\underline{\sf{Solution-}}$

The given inequality is as

$\rm :\longmapsto\:\dfrac{x}{x - 2} < 0$

$\rm :\longmapsto\:\dfrac{x}{x - 2} \times \dfrac{x - 2}{x - 2} < 0$

$\rm :\longmapsto\:\dfrac{x(x - 2)}{(x - 2)^{2} } < 0$

$\rm :\longmapsto\:x(x - 2) < 0$

$\rm :\longmapsto\:0 < x < 2$

$\bf\implies \:x \: \in \: (0, \: 2)$

The concept Used is

If p and q are two positive real numbers such that p < q and (x - p) (x - q) < 0 then p < x < q.