Question

How do you solve `(x+7)/(x-3)>0`?

Answer 1

The answer is `x in ]-oo, -7 [uu] 3, +oo[`

Explanation:

Let `f(x)=(x+7)/(x-3)`

Let's build the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaaa)` `-oo` `color(white)(aaaa)` `-7` `color(white)(aaaa)` `3` `color(white)(aaaaa)` `+oo`

`color(white)(aaaa)` `x+7` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `x-3` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

Therefore,

`f(x)>0` when `x in ]-oo, -7 [uu] 3, +oo[`