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

Jan 13, 2017

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

#### Explanation:

Let $f \left(a\right) = \frac{a}{a + 2}$

The domain of $f \left(a\right)$ is ${D}_{f} \left(a\right) = \mathbb{R} - \left\{- 2\right\}$

Let's do the sign chart

$\textcolor{w h i t e}{a a a a}$$a$$\textcolor{w h i t e}{a a a a a a a}$$\infty$$\textcolor{w h i t e}{a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a a}$$0$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$a + 2$$\textcolor{w h i t e}{a a a a a a}$$-$$\textcolor{w h i t e}{a a}$color(red)(∥)$\textcolor{w h i t e}{a a a}$$+$$\textcolor{w h i t e}{a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$a$$\textcolor{w h i t e}{a a a a a a a a a a}$$-$$\textcolor{w h i t e}{a a}$color(red)(∥)$\textcolor{w h i t e}{a a a}$$-$$\textcolor{w h i t e}{a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$f \left(a\right)$$\textcolor{w h i t e}{a a a a a a a}$$+$$\textcolor{w h i t e}{a a}$color(red)(∥)$\textcolor{w h i t e}{a a a}$$-$$\textcolor{w h i t e}{a a a}$$+$

Therefore,

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