Question

Solve the inequation:
${\displaystyle \frac{\text{x}+5}{\text{x}-3}<0}$

Answer 1

${\displaystyle \frac{\text{x}+5}{\text{x}-3}<0}$

We know that if ${\displaystyle \frac{\text{a}}{\text{b}}<0}$ when a > 0 and b < 0 or a < 0 and b > 0

∴ either x + 5 > 0 and x – 3 < 0
or x + 5 < 0 and x – 3 > 0
Case I:
x + 5 > 0 and x – 3 < 0
∴ x > – 5 and x < 3
∴ − 5 < x < 3
∴ solution set = (−5, 3)
Case II:
x + 5 < 0 and x – 3 > 0
∴ x  < – 5 and x > 3
which is not possible
∴ solution set = ø
∴  solution set of the given inequation is (– 5, 3)