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

Dec 11, 2016

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

#### Explanation:

Let $f \left(x\right) = \frac{x - 1}{x + 2}$

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

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

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{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}$$1$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x + 2$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a}$∣∣$\textcolor{w h i t e}{a}$$+$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$x - 1$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a}$∣∣$\textcolor{w h i t e}{a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a}$$+$$\textcolor{w h i t e}{a a a}$∣∣$\textcolor{w h i t e}{a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

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

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