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Question
Solve the inequation:
`("x" + 5)/("x" - 3) < 0`
Solution
`("x" + 5)/("x" - 3) < 0`
We know that if `"a"/"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)
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