# How do you solve #(x+5)/(x+2)<0#?

##### 1 Answer

#### Explanation:

A very stodgy mechanical way of looking at this is to say that the expression will be negative if either (x+5) < 0 or (x+2) < 0, but not both

so we look at these pairs

PAIR A

(x+5) < 0 **and** (x+2) > 0

this requires x < -5 and x > -2, so no solution

PAIR B

(x+5) > 0 **and** (x+2) < 0

this requires x > -5 and x < -2, so this solution works

further refining this approach, if x = 5, then the numerator is zero, not <0. so we must exclude x = 5

if x = -2, we have a singularity

so the complete answer appears to be

the obvious temptation here must to be to cross multiply ie to say that

if

then

but that doesn't work with inequalities. worth thinking about.