Write the number of integral solutions of .

Here, denominator i.e., x^{2} + 1 is always positive and not equal to zero. So, neglect it.

⇒ -x^{2} + 2x + 3 > 0

⇒ x^{2} – 2x – 3 < 0

⇒ (x – 3)(x + 1) < 0

Case I : (x – 3) < 0 and (x + 1) > 0

⇒ x < 3 and x > -1

By takin intersection x ∈ (-1, 3)

Case II : (x – 3) > 0 and (x + 1) < 0

⇒ x > 3 and x < -1

By taking intersection x ∈ ∅. So, case II is irrelevant.

So, the complete solution is x ∈ (-1, 3)

The integral solution is 0, 1 and 2. So, number of integral

solution is 3.

1