Question

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

Answer 1

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

Explanation:

Let `f(x)=(x-1)/(x+2)`

The domain of `f(x)` is `D_f(x)=RR-{-2}`

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

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-2` `color(white)(aaaa)` `1` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `x+2` `color(white)(aaaa)` `-` `color(white)(aaa)` `∣∣` `color(white)(a)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `x-1` `color(white)(aaaa)` `-` `color(white)(aaa)` `∣∣` `color(white)(a)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaa)` `+` `color(white)(aaa)` `∣∣` `color(white)(a)` `-` `color(white)(aaaa)` `+`

`f(x)<0` when `x in ] -2,1 [`

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