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

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Answer 1 · 2017-10-14T06:25:20

The solution is $a in (-oo,0) uu (1,+oo)$

Let $f(a)=(a-1)/a$

The sign chart is

$color(white)(aaaa)$ $a$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaaaaa)$ $0$ $color(white)(aaaaaaaa)$ $1$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $a$ $color(white)(aaaaaaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $a-1$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ #color(white)(aaaaa)-# $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(a)$ $color(white)(aaaaaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

Therefore,

$f(a)>0$ , when $a in (-oo,0) uu (1,+oo)$

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

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