Question

Solve the inequality `(y+4)/(1-y) > 0`?

Answer 1

The solution is `y in (-4,1)`

Explanation:

Let `f(y)=(y+4)/(1-y)`

Build a sign chart

`color(white)(aaaa)` `y` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-4` `color(white)(aaaaaa)` `1` `color(white)(aaaaa)` `+oo`

`color(white)(aaaa)` `y+4` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaaa)` `+` `color(white)(aaaa)`##

`color(white)(aaaa)` `1-y` `color(white)(aaaaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aa)` `||` `color(white)(aa)` `-`

`color(white)(aaaa)` `f(y)` `color(white)(aaaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aa)` `||` `color(white)(aa)` `-`

Therefore,

`f(y)>0` when `y in (-4,1)`

graph{(x+4)/(1-x) [-16.02, 16.02, -8.01, 8.01]}