Question

Solve the inequation:
`("x" - 2)/("x" + 5) > 0`

Answer 1

`("x" - 2)/("x" + 5) > 0`

If `"a"/"b" > 0`, then either a > 0 and b > 0 or a < 0 and b < 0
∴ either x − 2 > 0 and x + 5 > 0
or x − 2 < 0 and x + 5 < 0
Case I:
x – 2 > 0 and x + 5 > 0
∴ x > 2 and x > – 5
∴ x > 2
The solution set is `(2, ∞)`
Case II:
x – 2 < 0 and x + 5 < 0
∴ x < 2 and x < –5
x < –5
The solution set is `(- oo, -5)`
Combining both the cases, we can take solution set as `(-oo, -5) ∪ (2, oo)`