Question

solve the following inequation: x-5/x+2 is smaller than zero.​

Answer 1

Explanation:

(x+5)/(x+2)<0

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

3/(0^-) = - oo

so the complete answer appears to be

x in (-5, -2]

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

if

(x+5)/(x+2)<0

then

(x+5)/(x+2) * (x+2) < 0 * (x+2)

\implies x+5 <0, qquad x < -5

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

Hope it helps u.

Plz mark my answer as brainliest.