How do you solve $a/(a+2)>0$ using a sign chart?

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Answer 1 · 2017-01-13T18:04:03

The answer is $a in ] -oo,-2 [uu ] 0, +oo [$

Let $f(a)=a/(a+2)$

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

Let's do the sign chart

$color(white)(aaaa)$ $a$ $color(white)(aaaaaaa)$ $oo$ $color(white)(aaaa)$ $-2$ $color(white)(aaaaaa)$ $0$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $a+2$ $color(white)(aaaaaa)$ $-$ $color(white)(aa)$ $color(red)(∥)$ $color(white)(aaa)$ $+$ $color(white)(aaa)$ $+$

$color(white)(aaaa)$ $a$ $color(white)(aaaaaaaaaa)$ $-$ $color(white)(aa)$ $color(red)(∥)$ $color(white)(aaa)$ $-$ $color(white)(aaa)$ $+$

$color(white)(aaaa)$ $f(a)$ $color(white)(aaaaaaa)$ $+$ $color(white)(aa)$ $color(red)(∥)$ $color(white)(aaa)$ $-$ $color(white)(aaa)$ $+$

Therefore,

$f(a)>0$ when $a in ] -oo,-2 [uu ] 0, +oo [$

How do you solve a/(a+2)>0a/(a+2)>0 using a sign chart?