How do you solve $(x+3)/(x-1)>=0$ using a sign chart?

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Answer 1 · 2018-02-13T14:52:24

The solution is $x in (-oo,-3] uu(1,+oo)$

Let $f(x)=(x+3)/(x-1)$

Let's build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaa)$ $-3$ $color(white)(aaaaaaa)$ $1$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+3$ $color(white)(aaaaa)$ $-$ $color(white)(aaa)$ $0$ $color(white)(aaa)$ $+$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $x-1$ $color(white)(aaaaa)$ $-$ $color(white)(aaa)$ #color(white)(aaaa)-# $color(white)(aa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $+$ $color(white)(aaa)$ $0$ $color(white)(aaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aa)$ $+$

Therefore,

$f(x)>=0$ , when $x in (-oo,-3] uu(1,+oo)$

graph{(x+3)/(x-1) [-16.02, 16.01, -8.01, 8.01]}

How do you solve (x+3)/(x-1)>=0(x+3)/(x-1)>=0 using a sign chart?