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Question: The largest negative integer which satisfies \(\frac{x^{2} - 1}{(x - 2)(x - 3)} > 0\) is...

The largest negative integer which satisfies x2−1(x−2)(x−3)>0\frac{x^{2} - 1}{(x - 2)(x - 3)} > 0 is

A

– 4

B

–3

C

–1

D

–2

Answer

–2

Explanation

Solution

By wavy curve method.

x2−1(x−2)(x−3)>0\frac{x^{2} - 1}{(x - 2)(x - 3)} > 0 ⇒ x ∈ (–∞, –1) ∪ (1, 2) ∪ (3, ∞).

Therefore largest negative integer is –2