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प्रश्न
Solve `(x - 2)/(x + 5) > 2`.
उत्तर
We have, `(x - 2)/(x + 5) > 2`
⇒ `(x - 2)/(x + 5) - 2 > 0` .......[Subtracting 2 from each side]
⇒ `(-(x + 12))/(x + 5) > 0`
⇒ `(x + 12)/(x + 5) < 0` .......(Multiplying both sides by –1)
⇒ x + 12 > 0 and x + 5 < 0 .....[Since `a/b < 0` ⇒ a and b are of opposite signs.]
or
x + 12 < 0 and x + 5 > 0
⇒ x > –12 and x < –5
or
x < –12 and x > –5 .....(Not possible)
Therefore, –12 < x < –5 i.e. x ∈ (–12, –5).
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