# How do you solve (a-1)/a>0 using a sign chart?

Oct 14, 2017

The solution is $a \in \left(- \infty , 0\right) \cup \left(1 , + \infty\right)$

#### Explanation:

Let $f \left(a\right) = \frac{a - 1}{a}$

The sign chart is

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

$\textcolor{w h i t e}{a a a a}$$a - 1$$\textcolor{w h i t e}{a a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$color(white)(aaaaa)-$\textcolor{w h i t e}{a 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 a a}$$| |$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

Therefore,

$f \left(a\right) > 0$, when $a \in \left(- \infty , 0\right) \cup \left(1 , + \infty\right)$

graph{(x-1)/x [-16.02, 16.01, -8.01, 8.01]}