Question

CHAPTER → INEQUALITY

Q. x²+2x-3/x²+1 < 0

Answer 1

Given Equation is : (x^2 + 2x - 3)/(x^2 + 1) < 0.

= > (x - 1)(x + 3)/(x^2 + 1) < 0

Now, consider the numerator:

(1)

(i)

= > x - 1 = 0

= > x = 1


(ii) 

= > x - 1 = 0

= > x < 1


(iii)

= > x - 1 > 0

= > x > 1



(2) 

(i)

= > x + 3 = 0

= > x = -3.

(ii)

= > x + 3 < 0

= > x < -3


(iii)

= > x + 3 > 0

= > x > -3.


Now, consider the denominator:


= > x^2 + 1 > 0

= > x^2 > -1.


Therefore it lies between the range -3 < x < 1.


Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks