How do you solve $(x-1)/(x+2)<0$ ?

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Answer 1 · 2016-12-11T08:05:31

The answer is $=x in ] -2,1 [$

Let $f(x)=(x-1)/(x+2)$

The domain of $f(x)$ is $D_f(x)=RR-{-2}$

To solve the inequality, let's do a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-2$ $color(white)(aaaa)$ $1$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+2$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $∣∣$ $color(white)(a)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x-1$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $∣∣$ $color(white)(a)$ $-$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaa)$ $+$ $color(white)(aaa)$ $∣∣$ $color(white)(a)$ $-$ $color(white)(aaaa)$ $+$

$f(x)<0$ when $x in ] -2,1 [$

graph{(x-1)/(x+2) [-12.66, 12.65, -6.33, 6.33]}

How do you solve (x-1)/(x+2)<0(x-1)/(x+2)<0?