Question

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

Answer 1

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

Explanation:

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 [`