Question
Solve the inequations: $\frac{x-2}{x+5}>0$

Answer

$
\frac{x-2}{x+5}>0
$
Since $\frac{a}{b}>0$,
when $a>0$ and $b>0$ or $a<0$ and $b<0 b$
$\therefore$ either $x-2>0$ and $x+5>0$
or $x-2<0$ and $x+5<0$ Case $1: x-2>0$ and $x+5>0$
$\therefore x>2$ and $x>-5$
$\therefore \mathrm{x}>2$
$\therefore$ solution set $=(2, \infty)$
Case II:
$
\begin{aligned}
& x-2<0 \text { and } x+5<0 \\
& \therefore x<2 \text { and } x<-5 \\
& \therefore x<-5 \\
& \therefore \text { solution set }=(-\infty,-5)
\end{aligned}
$
$\therefore$ solution set $=(-\infty,-5)$
$\therefore$ the solution set of the given inequation is $(-\infty,-5) \cup(2, \infty)$

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